<?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>0001622302</rptOwnerCik>
            <rptOwnerName>Weiner Ross</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>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>Vice President and CFO</officerTitle>
        </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>5854</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F2"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Restricted Stock Units</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F3"/>
            </conversionOrExercisePrice>
            <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>2000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F5"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F4"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F4"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Shares</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>2000</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
                <value>Restricted Stock Units</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F3"/>
            </conversionOrExercisePrice>
            <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>2000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F7"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F6"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F6"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Shares</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>2000</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">33 1/3% of the shares vested on February 15, 2017.  An additional 33 1/3% of the shares were to vest on February 15, 2018 and the final 33 1/3% of the shares were to vest on February 15, 2019.</footnote>
        <footnote id="F2">All outstanding shares were disposed of in exchange for $18.00 per share pursuant to the Agreement and Plan of Merger (the &quot;Merger Agreement&quot;), dated as of January 23, 2017, by and among the Issuer, WestRock Company (&quot;WestRock&quot;) 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 (the &quot;Merger&quot;).</footnote>
        <footnote id="F3">Each restricted stock unit represented a contingent right to receive one Common Share of the Issuer.</footnote>
        <footnote id="F4">The restricted stock units were to vest in three equal annual installments, subject, with limited exceptions, to the Reporting Person's continued employment with the Issuer.</footnote>
        <footnote id="F5">Pursuant to the Merger Agreement, the restricted stock units that were outstanding as of immediately prior to the effective time of the Merger (&quot;MPS RSU&quot;) were assumed by WestRock and converted into an award of restricted stock units by WestRock with respect to a number of shares of common stock of WestRock, par value $0.01 per share (&quot;WestRock RSU&quot;), equal to (i) the number of common shares subject to the MPS RSU multiplied by (ii) the Exchange Ratio (as defined below), rounded to the nearest whole share.  Each WestRock RSU is subject to the same terms and conditions as were applicable to such MPS RSU.  &quot;Exchange Ratio&quot; means a fraction, the numerator of which is the Merger Consideration and the denominator of which is the average of the volume weighted average price per share of WestRock Common Stock on the New York Stock Exchange Inc. on each of the five consecutive trading days ending with the second complete trading day immediately prior to the closing date of the Merger.</footnote>
        <footnote id="F6">The restricted stock units vested on June 6, 2017, the closing date of the Merger, based on the Issuer's satisfaction of certain performance criteria.</footnote>
        <footnote id="F7">The restricted stock units were disposed of in exchange for $18.00 per share pursuant to the Merger Agreement multiplied by 150%, the applicable percentage based on certain performance criteria as measured on the closing date of the Merger.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Ross Weiner</signatureName>
        <signatureDate>2017-06-06</signatureDate>
    </ownerSignature>
</ownershipDocument>
