<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2019-01-25</periodOfReport>

    <notSubjectToSection16>1</notSubjectToSection16>

    <issuer>
        <issuerCik>0001179060</issuerCik>
        <issuerName>EnLink Midstream Partners, LP</issuerName>
        <issuerTradingSymbol>ENLK</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001664092</rptOwnerCik>
            <rptOwnerName>WSIP Egypt Holdings, LP</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>200 WEST STREET</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10282</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle></officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001663663</rptOwnerCik>
            <rptOwnerName>WSEP EGYPT HOLDINGS, LP</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>200 WEST STREET</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10282</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle></officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001663256</rptOwnerCik>
            <rptOwnerName>BROAD STREET INFRASTRUCTURE ADVISORS III, L.L.C.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>200 WEST STREET</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10282</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle></officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001663213</rptOwnerCik>
            <rptOwnerName>BROAD STREET ENERGY ADVISORS AIV-1, L.L.C.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>200 WEST STREET</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10282</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle></officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable></nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Series B Cumulative Convertible Preferred Units</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F3"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2019-01-25</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>J</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F3"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>58728994</value>
                    <footnoteId id="F3"/>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F3"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F3"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F3"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Units</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>0</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                    <footnoteId id="F3"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnotes</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                    <footnoteId id="F3"/>
                    <footnoteId id="F4"/>
                    <footnoteId id="F5"/>
                    <footnoteId id="F6"/>
                    <footnoteId id="F7"/>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">This statement is being filed by The Goldman Sachs Group, Inc. (&quot;GS Group&quot;), Goldman Sachs &amp; Co. LLC (&quot;Goldman Sachs&quot;), West Street International Infrastructure Partners III, L.P. (&quot;WS International&quot;), West Street European Infrastructure Partners III, L.P. (&quot;WS European&quot;), West Street Global Infrastructure Partners III, L.P. (&quot;WS Global&quot;), Broad Street Principal Investments, L.L.C. (&quot;BS Principal&quot;), West Street Energy Partners Offshore - B AIV-1, L.P. (&quot;WS Offshore B&quot;), West Street Energy Partners AIV-1, L.P. (&quot;WS AIV&quot;), West Street Energy Partners Offshore AIV-1, L.P. (&quot;WS Offshore AIV&quot;), West Street Energy Partners Offshore Holding - B AIV-1, L.P. (&quot;WS Holdings B&quot;), Broad Street Infrastructure Advisors III, L.L.C. (&quot;BS Infrastructure&quot;), (continued in footnote 2)</footnote>
        <footnote id="F2">and Broad Street Energy Advisors AIV-1, L.L.C. (&quot;BS Energy AIV&quot;, and together with WS International, WS European, WS Global, BS Principal, WS Offshore B, WS AIV, WS Offshore AIV, WS Holdings B and BS Infrastructure, the &quot;GS Entities&quot;), WSIP Egypt Holdings, LP (&quot;WSIP&quot;) and WSEP Egypt Holdings, LP (&quot;WSEP&quot;, and together with WSIP, GS Group, Goldman Sachs and the GS Entities, the &quot;Reporting Persons&quot;). Due to the electronic system's limitation of 10 Reporting Persons per joint filing, this statement is being filed in duplicate.</footnote>
        <footnote id="F3">On January 25, 2019, EnLink Midstream Partners, LP (the &quot;Issuer&quot;) became a wholly owned subsidiary of EnLink Midstream, LLC (&quot;ENLC&quot;) as the result of a merger between NOLA Merger Sub, LLC, a wholly owned subsidiary of ENLC, and the Issuer (the &quot;Merger&quot;).  In connection with the Merger, the Issuer entered into the Tenth Amended and Restated Agreement of Limited Partnership, which amended the terms of the Series B Cumulative Convertible Preferred Units (the &quot;Series B Units&quot;) to, among other things, make the Series B Units reported herein exchangeable for common units of ENLC at a ratio of 1 to 1.15 (subject to certain adjustments).  The Series B Units reported herein are no longer convertible into common units of the Issuer.</footnote>
        <footnote id="F4">The GS Entities are the direct or indirect beneficial owners of WSIP and WSEP, which hold 100 shares of common stock, and have appointed one of the two directors, of Enfield Holdings Advisors, Inc., which is the general partner of Enfield Holdings, L.P. (&quot;Holdings&quot;), which directly holds the Series B Preferred Units reported herein.</footnote>
        <footnote id="F5">Because of the relationship by and between the GS Entities, WSIP and WSEP on the one hand and Holdings on the other hand, the GS Entities, WSIP and WSEP may have been deemed (for purposes of Rule 13d-3(a) and Rule 16a-1(a) only and not for any other applicable purpose), to beneficially own the securities reported herein to the extent of the greater of their respective direct or indirect pecuniary interests in the profits or capital accounts of Holdings.</footnote>
        <footnote id="F6">For purposes of Rule 13d-3(a) and Rule 16a-1(a) only (and not for any other applicable purpose), GS Group and Goldman Sachs may have been deemed to beneficially own indirectly the securities reported herein to the extent of the greater of their respective direct or indirect pecuniary interests in the profits or capital accounts of Holdings, as (i) Goldman Sachs is an investment manager of certain of the GS Entities, (ii) Goldman Sachs is a subsidiary of GS Group, and (iii) affiliates of Goldman Sachs and GS Group are the general partner, managing limited partner, managing partner or investment manager of the GS Entities.</footnote>
        <footnote id="F7">The Reporting Persons disclaim beneficial ownership of the securities reported herein except to the extent of their pecuniary interest therein, if any, and this report shall not be deemed an admission that any such Reporting Person is the beneficial owner of, or has any pecuniary interests in, such securities for purposes of Section 16 of the Securities and Exchange Act of 1934, as amended, or for any other purpose.</footnote>
    </footnotes>

    <ownerSignature>
        <signatureName>WSIP Egypt Holdings, LP, By: Broad Street Infrastructure Advisors III, L.L.C., its General Partner, By: /s/ Yvette Kosic, Attorney-in-fact</signatureName>
        <signatureDate>2019-01-29</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>WSEP Egypt Holdings, LP, By: Broad Street Energy Advisors AIV-1, L.L.C., its General Partner, By: /s/ Yvette Kosic, Attorney-in-fact</signatureName>
        <signatureDate>2019-01-29</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>Broad Street Infrastructure Advisors III, L.L.C., By: /s/ Yvette Kosic, Attorney-in-fact</signatureName>
        <signatureDate>2019-01-29</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>Broad Street Energy Advisors AIV-1, L.L.C., By: /s/ Yvette Kosic, Attorney-in-fact</signatureName>
        <signatureDate>2019-01-29</signatureDate>
    </ownerSignature>
</ownershipDocument>
