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

    <schemaVersion>X0206</schemaVersion>

    <documentType>3</documentType>

    <periodOfReport>2017-10-31</periodOfReport>

    <noSecuritiesOwned>0</noSecuritiesOwned>

    <issuer>
        <issuerCik>0000819220</issuerCik>
        <issuerName>MULTI COLOR Corp</issuerName>
        <issuerTradingSymbol>LABL</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001720957</rptOwnerCik>
            <rptOwnerName>Constantia Flexibles Holding GmbH</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>HANDELSKAI 92, RIVERGATE</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>1200 VIENNA</rptOwnerCity>
            <rptOwnerState>C4</rptOwnerState>
            <rptOwnerZipCode></rptOwnerZipCode>
            <rptOwnerStateDescription>AUSTRIA</rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001721959</rptOwnerCik>
            <rptOwnerName>Constantia Lux SarL</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>5 RUE PIERRE D'ASPELT</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>GRAND-DUCHY OF LUXEMBOURG</rptOwnerCity>
            <rptOwnerState>N4</rptOwnerState>
            <rptOwnerZipCode>L-1142</rptOwnerZipCode>
            <rptOwnerStateDescription>LUXEMBOURG</rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001722011</rptOwnerCik>
            <rptOwnerName>Constantia Lux Parent S.A.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>5 RUE PIERRE D'ASPELT</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>GRAND-DUCHY OF LUXEMBOURG</rptOwnerCity>
            <rptOwnerState>N4</rptOwnerState>
            <rptOwnerZipCode>L-1142</rptOwnerZipCode>
            <rptOwnerStateDescription>LUXEMBOURG</rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001721938</rptOwnerCik>
            <rptOwnerName>Wendel SE</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>89 RUE TAITBOUT</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>PARIS 75009</rptOwnerCity>
            <rptOwnerState>I0</rptOwnerState>
            <rptOwnerZipCode></rptOwnerZipCode>
            <rptOwnerStateDescription>FRANCE</rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001722016</rptOwnerCik>
            <rptOwnerName>Wendel-Participations SE</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>89 RUE TAITBOUT</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>PARIS 75009</rptOwnerCity>
            <rptOwnerState>I0</rptOwnerState>
            <rptOwnerZipCode></rptOwnerZipCode>
            <rptOwnerStateDescription>FRANCE</rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>3383170</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                    <footnoteId id="F1"/>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>3383170</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                    <footnoteId id="F2"/>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnote</value>
                    <footnoteId id="F2"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>3383170</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                    <footnoteId id="F2"/>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnote</value>
                    <footnoteId id="F2"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>3383170</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                    <footnoteId id="F2"/>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnote</value>
                    <footnoteId id="F2"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>3383170</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                    <footnoteId id="F2"/>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnote</value>
                    <footnoteId id="F2"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Represents the amount of shares obtained by Constantia Flexibles Holding GmbH (&quot;CFlex Holding&quot;) in connection with the transactions contemplated by a Sale and Purchase Agreement, dated as of July 16, 2017 (the &quot;Sale and Purchase Agreement&quot;), by and among Multi-Color Corporation (&quot;MCC&quot;), Constantia Flexibles Germany GmbH, Constantia Flexibles International GmbH, CFlex Group (as defined below), and GPC Holdings B.V. Upon the consummation of the transaction contemplated by the Sale and Purchase Agreement on October 31, 2017 (the &quot;Sale&quot;), CFlex Holding received 3,383,170 shares of common stock, no par value, of MCC (the &quot;Common Stock&quot;), which represents 19.9% of MCC's shares of common stock issued and outstanding as of the close of business on July 16, 2017, the date of signing.</footnote>
        <footnote id="F2">Wendel-Participations SE holds approximately 36.66% of the share capital, and 50.13% of the exercisable voting rights (on the basis of the total number of shares and voting rights of Wendel SE as of September 30, 2017), and has the ability to appoint a majority of the members of the supervisory board, of Wendel SE, a French investment company. Wendel SE indirectly owns 60.78% of the equity and has the ability to nominate a majority of the directors, of Constantia Lux Parent S.A. (&quot;CFlex Parent&quot;). CFlex Parent is the sole equityholder of CFlex Lux.  Constantia Lux S.a r.l (&quot;CFlex Lux&quot;) is the sole equity holder and  has an ability to appoint a majority of the supervisory board, of CFlex Holding.  Accordingly, upon CFlex Germany's acquisition and the transfer of the Common Stock to CFlex Holding, each of Wendel-Participations SE, Wendel SE, CFlex Parent and CFlex Lux became an indirect beneficial owner of the Common Stock.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>CONSTANTIA FLEXIBLES HOLDING GMBH, By: /s/ Martin SchneeweiB, Name: Martin SchneeweiB, Title: By power of attorney</signatureName>
        <signatureDate>2017-11-09</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>CONSTANTIA LUX S.A R.L., By: /s/ Jean-Yves Hemery, Name: Jean-Yves Hemery, Title: Authorized Signatory, By: /s/ Charles Krombach, Name: Charles Krombach, Title: Authorized Signatory</signatureName>
        <signatureDate>2017-11-09</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>CONSTANTIA LUX PARENT S.A., By: /s/ Jean-Yves Hemery, Name: Jean-Yves Hemery, Title: Authorized Signatory, By: /s/ Charles Krombach, Name:  Charles Krombach, Title: Authorized Signatory</signatureName>
        <signatureDate>2017-11-09</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>WENDEL SE, By: /s/ Caroline Bertin Delacour, Name: Caroline Bertin Delacour, Title: Authorized Signatory</signatureName>
        <signatureDate>2017-11-09</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>WENDEL PARTICIPATIONS SE, By: /s/ Francois de Wendel, Name: Francois de Wendel, Title: Authorized Signatory</signatureName>
        <signatureDate>2017-11-09</signatureDate>
    </ownerSignature>
</ownershipDocument>
