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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2016-04-14</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001597264</issuerCik>
        <issuerName>Blueprint Medicines Corp</issuerName>
        <issuerTradingSymbol>BPMC</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001488495</rptOwnerCik>
            <rptOwnerName>Third Rock Ventures II, L.P.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O THIRD ROCK VENTURES, LLC</rptOwnerStreet1>
            <rptOwnerStreet2>29 NEWBURY STREET, 3RD FLOOR</rptOwnerStreet2>
            <rptOwnerCity>BOSTON</rptOwnerCity>
            <rptOwnerState>MA</rptOwnerState>
            <rptOwnerZipCode>02116</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001614061</rptOwnerCik>
            <rptOwnerName>Third Rock Ventures GP II, L.P.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>29 NEWBURY STREET, 3RD FLOOR</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>BOSTON</rptOwnerCity>
            <rptOwnerState>MA</rptOwnerState>
            <rptOwnerZipCode>02116</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001614073</rptOwnerCik>
            <rptOwnerName>TRV GP II, LLC</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>29 NEWBURY STREET, 3RD FLOOR</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>BOSTON</rptOwnerCity>
            <rptOwnerState>MA</rptOwnerState>
            <rptOwnerZipCode>02116</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001180428</rptOwnerCik>
            <rptOwnerName>LEVIN MARK J</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O THIRD ROCK VENTURES, LLC</rptOwnerStreet1>
            <rptOwnerStreet2>29 NEWBURY STREET, 3RD FLOOR</rptOwnerStreet2>
            <rptOwnerCity>BOSTON</rptOwnerCity>
            <rptOwnerState>MA</rptOwnerState>
            <rptOwnerZipCode>02116</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001192603</rptOwnerCik>
            <rptOwnerName>STARR KEVIN P</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O THIRD ROCK VENTURES, LLC</rptOwnerStreet1>
            <rptOwnerStreet2>29 NEWBURY STREET, 3RD FLOOR</rptOwnerStreet2>
            <rptOwnerCity>BOSTON</rptOwnerCity>
            <rptOwnerState>MA</rptOwnerState>
            <rptOwnerZipCode>02116</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001192595</rptOwnerCik>
            <rptOwnerName>TEPPER ROBERT I</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O THIRD ROCK VENTURES, LLC</rptOwnerStreet1>
            <rptOwnerStreet2>29 NEWBURY STREET, 3RD FLOOR</rptOwnerStreet2>
            <rptOwnerCity>BOSTON</rptOwnerCity>
            <rptOwnerState>MA</rptOwnerState>
            <rptOwnerZipCode>02116</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2016-04-14</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>1200000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>5453753</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                    <footnoteId id="F2"/>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">On April 14, 2016, Third Rock Ventures II, L.P. (&quot;TRV II&quot;) distributed, for no consideration, 1,200,000 shares of Common Stock of the Issuer (the &quot;Shares&quot;) to its limited partners and to Third Rock Ventures GP II, L.P. (&quot;TRV GP II&quot;), the general partner of TRV II, representing each such partner's pro rata interest in such Shares. On the same date, TRV GP II distributed, for no consideration, the Shares it received in the distribution by TRV II to its limited partners and to its general partner, TRV GP II, LLC (&quot;TRV GP II LLC&quot;), representing each such partner's pro rata interest in such Shares.  On the same date, TRV GP II LLC, distributed, for no consideration, the Shares it received in the distribution by TRV GP II to its members in an amount equal to each such member's respective pro rata interest in such Shares. All of the aforementioned distributions were made in accordance with the exemptions afforded by Rules 16a-13 and 16a-9 of the Securities Exchange Act of 1934, as amended.</footnote>
        <footnote id="F2">These shares are directly held by TRV II.  The general partner of TRV II is TRV GP II.  The general partner of TRV GP II is TRV GP II LLC.  The individual managers of TRV GP II LLC are Mark Levin (&quot;Levin&quot;), Kevin Starr (&quot;Starr&quot;) and Dr. Robert Tepper (&quot;Tepper&quot;).  Each of TRV GP II, TRV GP II LLC, Levin, Starr and Tepper disclaims beneficial ownership of the shares except to the extent of its or his pecuniary interest therein, if any, and this report shall not be deemed an admission that it or he is the beneficial owner of such shares.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Kevin Gillis, Chief Financial Officer of TRV GP II, LLC, general partner of Third Rock Ventures GP II, L.P., general partner of Third Rock Ventures II, L.P.</signatureName>
        <signatureDate>2016-04-15</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ Kevin Gillis, Chief Financial Officer of TRV GP II, LLC, general partner of Third Rock Ventures GP II, L.P.</signatureName>
        <signatureDate>2016-04-15</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ Kevin Gillis, Chief Financial Officer of TRV GP II, LLC</signatureName>
        <signatureDate>2016-04-15</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ Kevin Gillis by power of attorney for Mark Levin</signatureName>
        <signatureDate>2016-04-15</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ Kevin Gillis by power of attorney for Kevin Starr</signatureName>
        <signatureDate>2016-04-15</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ Kevin Gillis by power of attorney for Dr. Robert Tepper</signatureName>
        <signatureDate>2016-04-15</signatureDate>
    </ownerSignature>
</ownershipDocument>
