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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2020-03-27</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001488775</issuerCik>
        <issuerName>ClearBridge MLP &amp; Midstream Fund Inc.</issuerName>
        <issuerTradingSymbol>CEM</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0000005272</rptOwnerCik>
            <rptOwnerName>AMERICAN INTERNATIONAL GROUP INC</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>175 WATER STREET</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10038</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>1</isOther>
            <otherText>See Remarks</otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0000005108</rptOwnerCik>
            <rptOwnerName>AMERICAN GENERAL LIFE INSURANCE CO</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>2727-A ALLEN PARKWAY</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>HOUSTON</rptOwnerCity>
            <rptOwnerState>TX</rptOwnerState>
            <rptOwnerZipCode>77019</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>1</isOther>
            <otherText>See Remarks</otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>3.46% Senior Secured Notes Series I due 6/11/2025</value>
            </securityTitle>
            <transactionDate>
                <value>2020-03-27</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>J</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>393382.35</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>401323.86</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <valueOwnedFollowingTransaction>
                    <value>559610.20</value>
                </valueOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                    <footnoteId id="F2"/>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>Held through subsidiaries</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>3.56% Senior Secured Notes Series J due 6/11/2027</value>
            </securityTitle>
            <transactionDate>
                <value>2020-03-27</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>J</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>1049019.61</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>1070505.86</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <valueOwnedFollowingTransaction>
                    <value>1492293.86</value>
                </valueOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                    <footnoteId id="F3"/>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>Held through subsidiaries</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>3.76% Senior Secured Notes Series K due 6/11/2030</value>
            </securityTitle>
            <transactionDate>
                <value>2020-03-27</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>J</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>1442401.96</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>1472794.97</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <valueOwnedFollowingTransaction>
                    <value>2051901.06</value>
                </valueOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                    <footnoteId id="F4"/>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>Held through subsidiaries</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">The reported disposition was pursuant to a partial prepayment by the issuer at a price equal to the face value of the prepaid securities, plus accrued and unpaid interest, plus a pro rata portion of the make-whole amount with respect to the principal, calculated in accordance with the note purchase agreement, dated as of June 11, 2015.</footnote>
        <footnote id="F2">American General Life Insurance Company (&quot;AGLIC&quot;) and The Variable Annuity Life Insurance Company (&quot;VALIC&quot;), each an indirect wholly owned subsidiary of American International Group, Inc. (&quot;AIG&quot;), directly hold $373,073.46 principal amount and $186,536.74 principal amount, respectively, of the 3.46% Senior Secured Notes, Series I, due June 11, 2025 (the &quot;Series I Notes&quot;). AIG is an indirect beneficial owner of the Series I Notes.</footnote>
        <footnote id="F3">AGLIC directly holds $1,492,293.86 principal amount of the 3.56% Senior Secured Notes, Series J, due June 11, 2027 (the &quot;Series J Notes&quot;). AIG is an indirect beneficial owner of the Series J Notes.</footnote>
        <footnote id="F4">AGLIC and The United States Life Insurance Company in The City of New York directly hold $1,380,371.82 principal amount and $671,532.24 principal amount, respectively, of the 3.76% Senior Secured Notes, Series K, due June 11, 2030 (the &quot;Series K Notes&quot;). AIG is an indirect beneficial owner of the Series K Notes.</footnote>
    </footnotes>

    <remarks>Filed pursuant to Section 30(h) of the Investment Company Act of 1940.</remarks>

    <ownerSignature>
        <signatureName>/s/ Geoffrey N. Cornell, Authorized Signatory of American International Group, Inc.</signatureName>
        <signatureDate>2020-03-30</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ Julie A. Cotton Hearne, Authorized Signatory of American General Life Insurance Company</signatureName>
        <signatureDate>2020-03-30</signatureDate>
    </ownerSignature>
</ownershipDocument>
