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<p style="font: 10pt Times New Roman, Times, Serif; margin: 0; text-align: center"><b>UNITED STATES</b></p>

<p style="font: 10pt Times New Roman, Times, Serif; margin: 0; text-align: center"><b>SECURITIES AND EXCHANGE COMMISSION</b></p>

<p style="font: 10pt Times New Roman, Times, Serif; margin: 0; text-align: center"><b>Washington, D.C. 20549</b></p>



<p style="font: 10pt Times New Roman, Times, Serif; margin: 12pt 0 0; text-align: center"><b>FORM <span id="xdx_909_edei--DocumentType_c20230911__20230911_zEdOt8no2olb"><ix:nonNumeric contextRef="AsOf2023-09-11" name="dei:DocumentType">8-K</ix:nonNumeric></span></b></p>



<p style="font: 10pt Times New Roman, Times, Serif; margin: 12pt 0 0; text-align: center"><b>CURRENT REPORT</b></p>



<p style="font: 10pt Times New Roman, Times, Serif; margin: 12pt 0 0; text-align: center"><b>Pursuant to Section 13 or 15(d) of</b></p>

<p style="font: 10pt Times New Roman, Times, Serif; margin: 0; text-align: center"><b>the Securities Exchange Act of 1934</b></p>



<p style="font: 10pt Times New Roman, Times, Serif; margin: 12pt 0 0; text-align: center">Date of Report (Date of earliest event
reported):&#160;<b><span id="xdx_908_edei--DocumentPeriodEndDate_c20230911__20230911_zPiq6zSLLqNe"><ix:nonNumeric contextRef="AsOf2023-09-11" format="ixt:datemonthdayyearen" name="dei:DocumentPeriodEndDate">September 11, 2023</ix:nonNumeric></span></b></p>

<p style="font: 12pt Times New Roman, Times, Serif; margin: 0">&#160;</p>

<p style="font: 10pt Times New Roman, Times, Serif; margin: 0; text-align: center">______________________________</p>

<p style="font: 12pt Times New Roman, Times, Serif; margin: 0">&#160;</p>



<p style="font: 10pt Times New Roman, Times, Serif; margin: 0; text-align: center"><b><span id="xdx_90E_edei--EntityRegistrantName_c20230911__20230911_zR2nF2sSMMq2"><ix:nonNumeric contextRef="AsOf2023-09-11" name="dei:EntityRegistrantName">First Trust Energy Infrastructure Fund</ix:nonNumeric></span></b></p>

<p style="font: 10pt Times New Roman, Times, Serif; margin: 0; text-align: center">(Exact name of registrant as specified in its charter)</p>

<p style="font: 12pt Times New Roman, Times, Serif; margin: 0">&#160;</p>

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<p style="font: 10pt Times New Roman, Times, Serif; margin: 12pt 0 0; padding-top: 12pt; text-align: center">Registrant&#8217;s telephone number, including area
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<p style="font: 12pt Times New Roman, Times, Serif; text-align: center; margin-top: 0; margin-bottom: 0">&#160;</p>

<p style="font: 12pt Times New Roman, Times, Serif; text-align: center; margin-top: 0; margin-bottom: 0">____________________________________________</p>

<p style="font: 10pt Times New Roman, Times, Serif; margin: 0; text-align: center">(Former Name or Former Address, if Changed Since Last
Report.)</p>



<p style="font: 10pt Times New Roman, Times, Serif; margin: 12pt 0 0; text-align: justify">Check the appropriate box below if the Form&#160;8-K
filing is intended to simultaneously satisfy the filing obligation of the registrant under any of the following provisions (<i>see </i>General
Instruction&#160;A.2. below):</p>



<p style="font: 12pt Times New Roman, Times, Serif; margin: 12pt 0 0"><span style="font-family: Times New Roman, Times, Serif; font-size: 10pt"><span id="xdx_90C_edei--WrittenCommunications_c20230911__20230911_z1TIkLV5iRRg"><ix:nonNumeric contextRef="AsOf2023-09-11" format="ixt:booleanfalse" name="dei:WrittenCommunications">&#9744;</ix:nonNumeric></span></span><span style="font-family: Times New Roman, Times, Serif; font-size: 6pt">&#160;&#160;&#160;&#160;</span><span style="font-family: Times New Roman, Times, Serif; font-size: 10pt">Written
communications pursuant to Rule&#160;425 under the Securities Act (17 CFR 230.425)</span></p>



<p style="font: 12pt Times New Roman, Times, Serif; margin: 12pt 0 0"><span style="font-family: Times New Roman, Times, Serif; font-size: 10pt"><span id="xdx_90C_edei--SolicitingMaterial_c20230911__20230911_zdPya1yCdap6"><ix:nonNumeric contextRef="AsOf2023-09-11" format="ixt:booleanfalse" name="dei:SolicitingMaterial">&#9744;</ix:nonNumeric></span></span><span style="font-family: Times New Roman, Times, Serif; font-size: 6pt">&#160;&#160;&#160;&#160;</span><span style="font-family: Times New Roman, Times, Serif; font-size: 10pt">Soliciting
material pursuant to Rule&#160;14a-12 under the Exchange Act (17 CFR 240.14a-12)</span></p>



<p style="font: 12pt Times New Roman, Times, Serif; margin: 12pt 0 0"><span style="font-family: Times New Roman, Times, Serif; font-size: 10pt"><span id="xdx_900_edei--PreCommencementTenderOffer_c20230911__20230911_zeBlHznKN0fa"><ix:nonNumeric contextRef="AsOf2023-09-11" format="ixt:booleanfalse" name="dei:PreCommencementTenderOffer">&#9744;</ix:nonNumeric></span></span><span style="font-family: Times New Roman, Times, Serif; font-size: 6pt">&#160;&#160;&#160;&#160;</span><span style="font-family: Times New Roman, Times, Serif; font-size: 10pt">Pre-commencement
communications pursuant to Rule&#160;14d-2(b) under the Exchange Act
(17 CFR 240.14d-2(b))</span></p>



<p style="font: 12pt Times New Roman, Times, Serif; margin: 12pt 0 0"><span style="font-family: Times New Roman, Times, Serif; font-size: 10pt"><span id="xdx_90C_edei--PreCommencementIssuerTenderOffer_c20230911__20230911_zbeLEPTEQLlg"><ix:nonNumeric contextRef="AsOf2023-09-11" format="ixt:booleanfalse" name="dei:PreCommencementIssuerTenderOffer">&#9744;</ix:nonNumeric></span></span><span style="font-family: Times New Roman, Times, Serif; font-size: 6pt">&#160;&#160;&#160;&#160;</span><span style="font-family: Times New Roman, Times, Serif; font-size: 10pt">Pre-commencement
communications pursuant to Rule&#160;13e-4(c) under the Exchange Act
(17 CFR 240.13e-4(c))</span></p>



<p style="font: 12pt Times New Roman, Times, Serif; margin: 0; text-indent: 0.25in"></p><p style="text-align: justify; margin-top: 12pt">Indicate by check mark whether the registrant is an emerging growth company as defined in Rule 405 of the Securities Act of 1933 (&#167;230.405
of this chapter) or Rule 12b-2 of the Securities Exchange Act of 1934 (&#167;240.12b-2 of this chapter).</p>

<p style="text-align: left">Emerging growth company <span id="xdx_906_edei--EntityEmergingGrowthCompany_c20230911__20230911_zejTRvdse15j"><ix:nonNumeric contextRef="AsOf2023-09-11" format="ixt:booleanfalse" name="dei:EntityEmergingGrowthCompany">&#9744;</ix:nonNumeric></span></p>

<p style="text-align: justify">If an emerging growth company, indicate by check mark if the registrant has elected not to use the extended transition period for
complying with any new or revised financial accounting standards provided pursuant to Section 13(a) of the Exchange Act. &#9744;<span style="font-family: Times New Roman, Times, Serif; font-size: 10pt">&#160;</span></p>

<p style="font: 12pt Times New Roman, Times, Serif; margin: 0; text-indent: 0.25in"><span style="font-family: Times New Roman, Times, Serif; font-size: 10pt"></span></p>

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<p style="font: 12pt Times New Roman, Times, Serif; margin: 0; text-indent: 0.25in"><span style="font-family: Times New Roman, Times, Serif; font-size: 10pt"></span></p>

<p style="font: 12pt Times New Roman, Times, Serif; margin: 0">&#160;</p>

<table cellpadding="0" cellspacing="0" style="font: bold 10pt Times New Roman, Times, Serif; width: 100%; margin-top: 16pt; margin-bottom: 0"><tr style="vertical-align: top">
<td style="width: 0"></td><td style="width: 49.5pt"><span>Item</span>&#160;5.02</td><td>Departure of Directors or Certain Officers; Election of Directors; Appointment of Certain Officers; Compensatory Arrangements of Certain
Officers.</td></tr></table>

<p style="font: 10pt Times New Roman, Times, Serif; margin: 14pt 0 0; text-align: justify">First Trust Energy Infrastructure Fund <span style="font-family: Times New Roman, Times, Serif">(the
&#8220;Fund&#8221;) is filing herewith a press release issued on September 11, 2023, as Exhibit 99.1. The press release was issued by
First Trust Advisors L.P. to announce the appointment of Bronwyn Wright as a Trustee of the Fund, effective September 10, 2023. Details
regarding the appointment are contained in the press release included herein.</span></p>

<p style="font: 10pt Times New Roman, Times, Serif; margin: 14pt 0 0; text-align: justify">Ms. Wright has also been appointed as a member
of the Audit Committee, the Valuation Committee and the Nominating and Governance Committee for the Fund.</p>

<p style="font: 10pt Times New Roman, Times, Serif; margin: 14pt 0 0; text-align: justify">Ms. Wright is not currently a party to any
transaction with the Fund or First Trust Advisors L.P. that would require disclosure under Item 404(a) of Regulation S-K.</p>

<table cellpadding="0" cellspacing="0" style="font: bold 10pt Times New Roman, Times, Serif; width: 100%; margin-top: 16pt; margin-bottom: 0"><tr style="vertical-align: top">
<td style="width: 0"></td><td style="width: 49.5pt"><span>Item</span> 9.01</td><td><span>Financial
                                            Statements and Exhibits.</span></td></tr></table>

<p style="margin-top: 0; margin-bottom: 0">&#160;</p>

<table cellpadding="0" cellspacing="0" style="font: 10pt Times New Roman, Times, Serif; width: 100%; margin-top: 3pt; margin-bottom: 0"><tr style="vertical-align: top">
<td style="width: 0.5in">(d)</td><td style="width: 1in">Exhibits.</td><td></td></tr></table>


<p style="font: 10pt Times New Roman, Times, Serif; margin: 3pt 0">&#160;</p>

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    <td style="text-align: left; vertical-align: bottom; width: 12%"><span style="font-family: Times New Roman, Times, Serif; font-size: 10pt"><b>Exhibit</b></span></td>
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    <td style="width: 85%; padding-right: 5.4pt; padding-left: 5.4pt">&#160;</td></tr>
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    <td style="border-bottom: Black 1pt solid; text-align: left; vertical-align: bottom"><span style="font-family: Times New Roman, Times, Serif; font-size: 10pt"><b>Number</b></span></td>
    <td style="padding-right: 5.4pt; padding-left: 5.4pt">&#160;</td>
    <td style="border-bottom: Black 1pt solid; padding-right: 5.4pt"><span style="font-family: Times New Roman, Times, Serif; font-size: 10pt"><b>Description</b></span></td></tr>
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    <td style="text-align: left; padding-right: 5.4pt; vertical-align: bottom"><span style="font-family: Times New Roman, Times, Serif; font-size: 10pt"><a href="ex_99.htm">Press release of First Trust Advisors L.P. dated September 11, 2023</a>.</span></td></tr>
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<p style="font: 10pt Times New Roman, Times, Serif; margin: 3pt 0 0 1.5in; text-indent: -1.5in">&#160;</p>

<p style="font: 10pt Times New Roman, Times, Serif; margin: 3pt 0 0 1.5in; text-indent: -1.5in"></p>



<p style="font: 10pt Times New Roman, Times, Serif; margin: 14pt 0 0; text-align: center"><b>SIGNATURES</b></p>

<p style="font: 10pt Times New Roman, Times, Serif; margin: 14pt 0 0; text-align: justify">Pursuant to the requirements of the Securities
Exchange Act of 1934, the registrant has duly caused this report to be signed on its behalf by the undersigned hereunto duly authorized.</p>

<p style="font: 12pt/14pt Times New Roman, Times, Serif; margin: 0 0 0 3.5in; text-indent: -3.5in">&#160;</p>

<p style="font: 12pt/14pt Times New Roman, Times, Serif; margin: 0 0 0 3.5in; text-indent: -3.5in">&#160;</p>


<table cellspacing="0" cellpadding="0" style="font: 10pt Times New Roman, Times, Serif; width: 100%; border-collapse: collapse">
  <tr style="vertical-align: top">
    <td>Dated: September 12, 2023</td>
    <td style="padding-right: 5.4pt; text-indent: 0in; line-height: 14pt">&#160;</td>
    <td style="padding-right: 5.4pt; text-indent: 0in; line-height: 14pt"><b>FIRST TRUST ENERGY INFRASTRUCTURE FUND</b></td></tr>
  <tr style="vertical-align: top">
    <td>&#160;</td>
    <td style="padding-right: 5.4pt; text-indent: 0in; line-height: 14pt">&#160;</td>
    <td style="padding-right: 5.4pt; text-indent: 0in; line-height: 14pt">&#160;</td></tr>
  <tr style="vertical-align: top">
    <td style="width: 50%">&#160;</td>
    <td style="width: 5%; padding-right: 5.4pt; text-indent: 0in; line-height: 14pt"><span style="font-family: Times New Roman, Times, Serif; font-size: 10pt">By:</span></td>
    <td style="border-bottom: Black 1pt solid; width: 45%; padding-right: 5.4pt; text-indent: 0in; line-height: 14pt"><span style="font-family: Times New Roman, Times, Serif; font-size: 10pt">/s/ W. Scott Jardine</span></td></tr>
  <tr style="vertical-align: top">
    <td>&#160;</td>
    <td style="padding-right: 5.4pt; text-indent: 0in; line-height: 14pt"><span style="font-family: Times New Roman, Times, Serif; font-size: 10pt">Name</span></td>
    <td style="padding-right: 5.4pt; text-indent: 0in; line-height: 14pt"><span style="font-family: Times New Roman, Times, Serif; font-size: 10pt">W. Scott Jardine</span></td></tr>
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    <td>&#160;</td>
    <td style="padding-right: 5.4pt; text-indent: 0in; line-height: 14pt"><span style="font-family: Times New Roman, Times, Serif; font-size: 10pt">Title:</span></td>
    <td style="padding-right: 5.4pt; text-indent: 0in; line-height: 14pt"><span style="font-family: Times New Roman, Times, Serif; font-size: 10pt">Secretary</span></td></tr>
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<p style="font: 10pt Times New Roman, Times, Serif; margin: 14pt 0 0; text-align: justify">&#160;</p>

<p style="font: 10pt Times New Roman, Times, Serif; margin: 14pt 0 0; text-align: justify"></p>

<p style="font: 10pt Times New Roman, Times, Serif; margin: 14pt 0 0; text-align: center"><b>EXHIBIT INDEX</b></p>

<p style="font: 8pt Times New Roman, Times, Serif; margin: 0pt 0 0; text-align: justify"></p>



<p style="font: 10pt Times New Roman, Times, Serif; margin: 3pt 0 0 1.5in; text-indent: -1.5in">&#160;</p>

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    <td style="text-align: left; vertical-align: bottom; width: 12%"><span style="font-family: Times New Roman, Times, Serif; font-size: 10pt"><b>Exhibit</b></span></td>
    <td style="width: 3%; padding-right: 5.4pt; padding-left: 5.4pt">&#160;</td>
    <td style="width: 85%; padding-right: 5.4pt; padding-left: 5.4pt">&#160;</td></tr>
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    <td style="border-bottom: Black 1pt solid; text-align: left; vertical-align: bottom"><span style="font-family: Times New Roman, Times, Serif; font-size: 10pt"><b>Number</b></span></td>
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    <td style="border-bottom: Black 1pt solid; padding-right: 5.4pt"><span style="font-family: Times New Roman, Times, Serif; font-size: 10pt"><b>Description</b></span></td></tr>
  <tr style="vertical-align: top">
    <td style="text-align: left; padding-right: 5.4pt; vertical-align: bottom"><span style="font-family: Times New Roman, Times, Serif; font-size: 10pt">99.1</span></td>
    <td style="padding-right: 5.4pt; padding-left: 5.4pt">&#160;</td>
    <td style="text-align: left; padding-right: 5.4pt; vertical-align: bottom"><span style="font-family: Times New Roman, Times, Serif; font-size: 10pt"><a href="ex_99.htm">Press release of First Trust Advisors L.P. dated September 11, 2023.</a></span></td></tr>
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[{"type": "8-K", "sequence": "1", "filename": "fif_8k.htm", "description": "CURRENT REPORT", "secsgml_size_bytes": 24211}]
{"company-data": {"conformed-name": "FIRST TRUST ENERGY INFRASTRUCTURE FUND", "cik": "0001513789", "irs-number": "452751056", "fiscal-year-end": "1130"}, "filing-values": {"form-type": "8-K", "act": "34", "file-number": "811-22528", "film-number": "231250314"}, "business-address": {"street1": "120 EAST LIBERTY DRIVE, SUITE 400", "city": "WHEATON", "state": "IL", "zip": "60187", "phone": "630-765-8000"}, "mail-address": {"street1": "120 EAST LIBERTY DRIVE, SUITE 400", "city": "WHEATON", "state": "IL", "zip": "60187"}}
UNITED STATES
SECURITIES AND EXCHANGE COMMISSION
Washington, D.C. 20549
FORM
8-K
CURRENT REPORT
Pursuant to Section 13 or 15(d) of
the Securities Exchange Act of 1934
Date of Report (Date of earliest event
reported):
September 11, 2023
______________________________
First Trust Energy Infrastructure Fund
(Exact name of registrant as specified in its charter)
Massachusetts
811-22528
45-2751056
(State or other jurisdiction
(Commission File Number)
(IRS Employer
of incorporation)
Identification No.)
120 East Liberty Drive
,
Suite 400
Wheaton
,
Illinois
(Address of principal executive offices)
60187
(zip code)
Registrant's telephone number, including area
code: (
630
)
765-8000
____________________________________________
(Former Name or Former Address, if Changed Since Last
Report.)
Check the appropriate box below if the Form 8-K
filing is intended to simultaneously satisfy the filing obligation of the registrant under any of the following provisions (
see
General
Instruction A.2. below):
☐
Written
communications pursuant to Rule 425 under the Securities Act (17 CFR 230.425)
☐
Soliciting
material pursuant to Rule 14a-12 under the Exchange Act (17 CFR 240.14a-12)
☐
Pre-commencement
communications pursuant to Rule 14d-2(b) under the Exchange Act
(17 CFR 240.14d-2(b))
☐
Pre-commencement
communications pursuant to Rule 13e-4(c) under the Exchange Act
(17 CFR 240.13e-4(c))
Indicate by check mark whether the registrant is an emerging growth company as defined in Rule 405 of the Securities Act of 1933 (§230.405
of this chapter) or Rule 12b-2 of the Securities Exchange Act of 1934 (§240.12b-2 of this chapter).
Emerging growth company
☐
If an emerging growth company, indicate by check mark if the registrant has elected not to use the extended transition period for
complying with any new or revised financial accounting standards provided pursuant to Section 13(a) of the Exchange Act. ☐
Item
5.02
Departure of Directors or Certain Officers; Election of Directors; Appointment of Certain Officers; Compensatory Arrangements of Certain
Officers.
First Trust Energy Infrastructure Fund
(the
"Fund") is filing herewith a press release issued on September 11, 2023, as Exhibit 99.1. The press release was issued by
First Trust Advisors L.P. to announce the appointment of Bronwyn Wright as a Trustee of the Fund, effective September 10, 2023. Details
regarding the appointment are contained in the press release included herein.
Ms. Wright has also been appointed as a member
of the Audit Committee, the Valuation Committee and the Nominating and Governance Committee for the Fund.
Ms. Wright is not currently a party to any
transaction with the Fund or First Trust Advisors L.P. that would require disclosure under Item 404(a) of Regulation S-K.
Item
9.01
Financial
                                            Statements and Exhibits.
(d)
Exhibits.
Exhibit
Number
Description
99.1
Press release of First Trust Advisors L.P. dated September 11, 2023
.
SIGNATURES
Pursuant to the requirements of the Securities
Exchange Act of 1934, the registrant has duly caused this report to be signed on its behalf by the undersigned hereunto duly authorized.
Dated: September 12, 2023
FIRST TRUST ENERGY INFRASTRUCTURE FUND
By:
/s/ W. Scott Jardine
Name
W. Scott Jardine
Title:
Secretary
EXHIBIT INDEX
Exhibit
Number
Description
99.1
Press release of First Trust Advisors L.P. dated September 11, 2023.