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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2022-06-16</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001534992</issuerCik>
        <issuerName>Fiesta Restaurant Group, Inc.</issuerName>
        <issuerTradingSymbol>FRGI</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001511425</rptOwnerCik>
            <rptOwnerName>RAUCH STACEY</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O FIESTA RESTAURANT GROUP, INC.</rptOwnerStreet1>
            <rptOwnerStreet2>14800 LANDMARK BOULEVARD, SUITE 500</rptOwnerStreet2>
            <rptOwnerCity>DALLAS</rptOwnerCity>
            <rptOwnerState>TX</rptOwnerState>
            <rptOwnerZipCode>75254</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock, par value $0.01 per share</value>
            </securityTitle>
            <transactionDate>
                <value>2022-06-16</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>13992</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                    <footnoteId id="F1"/>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>64092</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">The shares were granted to the Reporting Person pursuant to the Issuer's 2021 Stock Incentive Plan. The stock award reported herein shall vest (and the restrictions shall lapse) in full on June 16, 2023, provided that the Reporting Person has continuously remained a director of the Issuer. Any unvested shares underlying the stock award reported herein will be immediately forfeited upon the Reporting Person ceasing to be a director. The stock award reported herein is not transferable unless vested.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>By:  /s/ Stacey Rauch</signatureName>
        <signatureDate>2022-06-21</signatureDate>
    </ownerSignature>
</ownershipDocument>
