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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2017-06-06</periodOfReport>

    <notSubjectToSection16>1</notSubjectToSection16>

    <issuer>
        <issuerCik>0001645926</issuerCik>
        <issuerName>Multi Packaging Solutions International Ltd</issuerName>
        <issuerTradingSymbol>MPSX</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001245966</rptOwnerCik>
            <rptOwnerName>SOULELES THOMAS S</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O MULTI PACKAGING SOLUTIONS INTL. LTD.</rptOwnerStreet1>
            <rptOwnerStreet2>885 THIRD AVENUE, 28TH FLOOR</rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10022</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Shares</value>
            </securityTitle>
            <transactionDate>
                <value>2017-06-06</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>D</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>23482216</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Mustang Investment Holdings L.P.</value>
                    <footnoteId id="F2"/>
                    <footnoteId id="F3"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Disposed of in exchange for $18.00 per share pursuant to the Agreement and Plan of Merger, dated as of January 23, 2017, by and among the Issuer, WestRock Company and WRK Merger Sub Limited (&quot;Merger Sub&quot;), pursuant to which Merger Sub was merged with and into the Issuer, with the Issuer surviving such merger.</footnote>
        <footnote id="F2">The reported shares were held by Mustang Investment Holdings L.P. (&quot;Mustang Holdings&quot;).  MDP Global Investors II Limited (&quot;MDP Limited&quot;) is the general partner of Mustang Holdings.  Mr. Souleles is a member and officer of MDP Limited.</footnote>
        <footnote id="F3">As a result of the relationships described in footnote 2, each of MDP Limited and Mr. Souleles may have been deemed to share beneficial ownership of the reported shares.  Each of MDP Limited and Mr. Souleles hereby disclaims beneficial ownership of such shares, except to the extent of their respective pecuniary interests therein.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Thomas S. Souleles</signatureName>
        <signatureDate>2017-06-06</signatureDate>
    </ownerSignature>
</ownershipDocument>
