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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2015-10-27</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001655362</rptOwnerCik>
            <rptOwnerName>Copans Richard Harris</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O MULTI PACKAGING SOLUTIONS INTL. LTD.</rptOwnerStreet1>
            <rptOwnerStreet2>150 E 52ND ST, 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 Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2015-10-27</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>1737500</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>12.2525</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>29232216</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnote</value>
                    <footnoteId id="F2"/>
                    <footnoteId id="F3"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Represents shares of Multi Packaging Solutions International Limited stock sold pursuant to an underwritten initial public offering.</footnote>
        <footnote id="F2">The reported shares are 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. Copans is an officer of MDP Limited.</footnote>
        <footnote id="F3">As a result of the relationships described in footnote 2, each of MDP Limited and Mr. Copans may be deemed to share beneficial ownership of the reported shares.  Each of MDP Limited and Mr. Copans hereby disclaims beneficial ownership of such shares, except to the extent of their respective pecuniary interests therein.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Richard H. Copans</signatureName>
        <signatureDate>2015-10-27</signatureDate>
    </ownerSignature>
</ownershipDocument>
