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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2020-09-28</periodOfReport>

    <notSubjectToSection16>1</notSubjectToSection16>

    <issuer>
        <issuerCik>0001510487</issuerCik>
        <issuerName>Principia Biopharma Inc.</issuerName>
        <issuerTradingSymbol>PRNB</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001595117</rptOwnerCik>
            <rptOwnerName>George Simeon</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O SR ONE CAPITAL MANAGEMENT, LP</rptOwnerStreet1>
            <rptOwnerStreet2>161 WASHINGTON STREET, SUITE 500</rptOwnerStreet2>
            <rptOwnerCity>CONSHOHOCKEN</rptOwnerCity>
            <rptOwnerState>PA</rptOwnerState>
            <rptOwnerZipCode>19428</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

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                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2020-09-28</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>U</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>2982855</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>100.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
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                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
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                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnote</value>
                    <footnoteId id="F2"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable>
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                <transactionShares>
                    <value>28623</value>
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                <transactionPricePerShare>
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                </transactionAcquiredDisposedCode>
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            <exerciseDate>
                <footnoteId id="F3"/>
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            <expirationDate>
                <value>2022-12-29</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
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                </underlyingSecurityShares>
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                <natureOfOwnership>
                    <value>See Footnote</value>
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                </natureOfOwnership>
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        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
                <value>Director Stock Option (right to buy)</value>
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                <value>17.00</value>
                <footnoteId id="F4"/>
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            <transactionDate>
                <value>2020-09-28</value>
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            <deemedExecutionDate></deemedExecutionDate>
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            <transactionTimeliness>
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            <exerciseDate>
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            <expirationDate>
                <value>2028-09-12</value>
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                <underlyingSecurityTitle>
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            <transactionTimeliness>
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                <transactionShares>
                    <value>10240</value>
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                <transactionPricePerShare>
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                <transactionAcquiredDisposedCode>
                    <value>D</value>
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            <exerciseDate>
                <footnoteId id="F4"/>
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            <expirationDate>
                <value>2029-06-10</value>
            </expirationDate>
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                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>10240</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
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                    <value>0</value>
                </sharesOwnedFollowingTransaction>
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        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
                <value>Director Stock Option (right to buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>62.66</value>
                <footnoteId id="F4"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2020-09-28</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
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                <transactionFormType>4</transactionFormType>
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                <equitySwapInvolved>0</equitySwapInvolved>
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            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>10240</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F4"/>
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                <transactionAcquiredDisposedCode>
                    <value>D</value>
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            <exerciseDate>
                <footnoteId id="F4"/>
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            <expirationDate>
                <value>2030-06-03</value>
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            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>10240</value>
                </underlyingSecurityShares>
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                    <value>0</value>
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        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Pursuant to the Agreement and Plan of Merger, dated as of August 16, 2020, by and among Principia Biopharma Inc. (the &quot;Issuer&quot;), Sanofi (&quot;Sanofi&quot;) and Kortex Acquisition Corp. (&quot;Purchaser&quot;) (the &quot;Merger Agreement&quot;), on September 28, 2020, Purchaser merged with and into the Issuer, with the Issuer continuing as the surviving corporation and a wholly owned subsidiary of Sanofi (the &quot;Merger&quot;). At the effective time of the Merger (the &quot;Effective Time&quot;), these shares were canceled in exchange for $100.00 per share (the &quot;Offer Price&quot;) in cash, without interest and subject to any applicable withholding taxes.</footnote>
        <footnote id="F2">S.R. One, Limited, an indirect, wholly-owned subsidiary of GlaxoSmithKline plc, is the record holder of these shares reported herein. Simeon J. George is the CEO &amp; Managing Partner of SR One Capital Management LP and as of September 14, 2020 was Chief Executive Officer, President and a Member of the Board of Trustees at S.R. One, Limited and an employee of GlaxoSmithKline LLC, an indirect, wholly-owned subsidiary of GlaxoSmithKline plc. Dr. George disclaims beneficial ownership of all shares held by S.R. One, Limited and this report shall not be deemed an admission of beneficial ownership of such shares for the purpose of Section 16 or for any other purpose except to the extent of his pecuniary interest therein.</footnote>
        <footnote id="F3">Pursuant to the Merger Agreement, at the Effective Time, each warrant was converted into the right to receive the Offer Price less the applicable exercise price per share of such warrant.</footnote>
        <footnote id="F4">Pursuant to the Merger Agreement, at the Effective Time, each of the unvested and outstanding options was accelerated and became fully vested, and each of the outstanding options was canceled and converted into the right to receive a cash amount equal to the product of (i) the number of shares that are subject to such options, multiplied by (ii) the excess (if any) of (x) the Offer Price over (y) the exercise price payable per share under such options.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Christopher Y. Chai, Attorney-in-Fact for Simeon J. George</signatureName>
        <signatureDate>2020-09-28</signatureDate>
    </ownerSignature>
</ownershipDocument>
