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

    <schemaVersion>X0508</schemaVersion>

    <documentType>4/A</documentType>

    <periodOfReport>2022-09-12</periodOfReport>

    <dateOfOriginalSubmission>2024-07-04</dateOfOriginalSubmission>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001698022</issuerCik>
        <issuerName>Farmers &amp; Merchants Bancshares, Inc.</issuerName>
        <issuerTradingSymbol>FMFG</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001958843</rptOwnerCik>
            <rptOwnerName>RENBAUM CAROL ELLEN</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>3921 BUTLER ROAD</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>REISTERSTOWN</rptOwnerCity>
            <rptOwnerState>MD</rptOwnerState>
            <rptOwnerZipCode>21136</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001631680</rptOwnerCik>
            <rptOwnerName>RENBAUM BARRY J.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>3921 BUTLER ROAD</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>REISTERSTOWN</rptOwnerCity>
            <rptOwnerState>MD</rptOwnerState>
            <rptOwnerZipCode>21136</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <aff10b5One>0</aff10b5One>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2025-07-25</value>
            </transactionDate>
            <deemedExecutionDate>
                <value>2025-07-25</value>
            </deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>J</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>6853</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>16.43</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>321472</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Reporting Persons' joint purchase of 6853 shares of Issuer's common stock on July 25, 2025 referenced in Table 1 was executed by the administrator of, and pursuant to, Issuer's dividend-reinvestment plan.</footnote>
    </footnotes>

    <remarks>The object of this submission is to clarify the nature of the transaction reported by the Reporting Persons in Form 4 filed with the Commission on August 4, 2025; namely, that their acquisition of 6853 shares of Issuer's common stock on July 25, 2025 was attributable to stock purchases executed pursuant to the company's dividend-reinvestment plan.</remarks>

    <ownerSignature>
        <signatureName>Barry J. Renbaum</signatureName>
        <signatureDate>2025-08-08</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>Carol E. Renbaum</signatureName>
        <signatureDate>2025-08-08</signatureDate>
    </ownerSignature>
</ownershipDocument>
