<?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>0001435618</rptOwnerCik>
            <rptOwnerName>Babler Martin</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O PRINCIPIA BIOPHARMA INC.</rptOwnerStreet1>
            <rptOwnerStreet2>220 E. GRAND AVENUE</rptOwnerStreet2>
            <rptOwnerCity>SOUTH SAN FRANCISCO</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>94080</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>President, CEO</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

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            </securityTitle>
            <transactionDate>
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            <deemedExecutionDate></deemedExecutionDate>
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                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
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                    <footnoteId id="F2"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>100.00</value>
                </transactionPricePerShare>
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                </transactionAcquiredDisposedCode>
            </transactionAmounts>
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                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
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                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2020-09-28</value>
            </transactionDate>
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            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
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                </transactionShares>
                <transactionPricePerShare>
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                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
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            </transactionAmounts>
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            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
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                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnote</value>
                    <footnoteId id="F3"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
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            <deemedExecutionDate></deemedExecutionDate>
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                </transactionShares>
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                <natureOfOwnership>
                    <value>See footnote</value>
                    <footnoteId id="F4"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable>
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            </securityTitle>
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            </conversionOrExercisePrice>
            <transactionDate>
                <value>2020-09-28</value>
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            <deemedExecutionDate></deemedExecutionDate>
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                </underlyingSecurityTitle>
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                </underlyingSecurityShares>
            </underlyingSecurity>
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                    <value>See footnote</value>
                    <footnoteId id="F4"/>
                </natureOfOwnership>
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        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
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            <transactionDate>
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            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
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                <transactionPricePerShare>
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            <expirationDate>
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            </expirationDate>
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                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
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        <derivativeTransaction>
            <securityTitle>
                <value>Employee Stock Option (right to buy)</value>
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            <transactionDate>
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                <transactionPricePerShare>
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                </underlyingSecurityTitle>
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        <derivativeTransaction>
            <securityTitle>
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            </securityTitle>
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            <transactionTimeliness>
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                </transactionShares>
                <transactionPricePerShare>
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            <expirationDate>
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            <underlyingSecurity>
                <underlyingSecurityTitle>
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        <derivativeTransaction>
            <securityTitle>
                <value>Employee Stock Option (right to buy)</value>
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            <transactionTimeliness>
                <value></value>
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            <transactionAmounts>
                <transactionShares>
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                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F6"/>
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                <transactionAcquiredDisposedCode>
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                </underlyingSecurityTitle>
                <underlyingSecurityShares>
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            <securityTitle>
                <value>Employee Stock Option (right to buy)</value>
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            <transactionTimeliness>
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                    <value>187144</value>
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                <transactionPricePerShare>
                    <footnoteId id="F6"/>
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                <transactionAcquiredDisposedCode>
                    <value>D</value>
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            <exerciseDate>
                <footnoteId id="F6"/>
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            <expirationDate>
                <value>2028-08-23</value>
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            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
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                <directOrIndirectOwnership>
                    <value>D</value>
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        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
                <value>Employee Stock Option (right to buy)</value>
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                <footnoteId id="F6"/>
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            <transactionTimeliness>
                <value></value>
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            <transactionAmounts>
                <transactionShares>
                    <value>155000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F6"/>
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                <transactionAcquiredDisposedCode>
                    <value>D</value>
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            <exerciseDate>
                <footnoteId id="F6"/>
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            <expirationDate>
                <value>2029-02-28</value>
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                <underlyingSecurityTitle>
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                <underlyingSecurityShares>
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                </underlyingSecurityShares>
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                <sharesOwnedFollowingTransaction>
                    <value>0</value>
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                <directOrIndirectOwnership>
                    <value>D</value>
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        <derivativeTransaction>
            <securityTitle>
                <value>Employee Stock Option (right to buy)</value>
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            <conversionOrExercisePrice>
                <value>67.31</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2020-09-28</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>D</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F6"/>
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            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>200000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F6"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
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            <exerciseDate>
                <footnoteId id="F6"/>
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            <expirationDate>
                <value>2030-03-04</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>200000</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
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                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
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            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</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 in cash, without interest and subject to any applicable withholding taxes.</footnote>
        <footnote id="F2">Includes 213 shares acquired under the Employment Stock Purchase Plan on September 25, 2020.</footnote>
        <footnote id="F3">Shares indirectly held by Babler Trust Agreement Dated October 25, 2006, of which the Reporting Person is a trustee and may be deemed to share voting and dispositive power over these shares.</footnote>
        <footnote id="F4">Shares indirectly held by Martin Babler, as custodian for his minor children under California Uniform Transfer to Minors Act, of which the Reporting Person is a custodian and may be deemed to share voting and dispositive power over these shares.</footnote>
        <footnote id="F5">Pursuant to the Merger Agreement, at the Effective Time, each warrant was converted into the right to receive $100.00 less the applicable exercise price per share of such warrant.</footnote>
        <footnote id="F6">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) $100.00 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 Martin Babler</signatureName>
        <signatureDate>2020-09-28</signatureDate>
    </ownerSignature>
</ownershipDocument>
