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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2016-01-15</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000949870</issuerCik>
        <issuerName>BOSTON BEER CO INC</issuerName>
        <issuerTradingSymbol>SAM</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001543082</rptOwnerCik>
            <rptOwnerName>Lim Ai-Li</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O THE BOSTON BEER COMPANY</rptOwnerStreet1>
            <rptOwnerStreet2>1 DESIGN CENTER PLACE, STE. 850</rptOwnerStreet2>
            <rptOwnerCity>BOSTON</rptOwnerCity>
            <rptOwnerState>MA</rptOwnerState>
            <rptOwnerZipCode>02210</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>V.P. of Human Resources</officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Class A Common</value>
            </securityTitle>
            <transactionDate>
                <value>2016-01-15</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>123</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>141.34</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>408</value>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">The shares were purchased pursuant to the Issuer's Employee Equity Incentive Plan on January 15, 2016, with an effective grant date of January 1, 2016. Under this plan, tenured employees may purchase restricted shares at a discounted price. These restricted shares vest in five equal installments over a five year period, provided that the Reporting Person remains employed by the Issuer as of the applicable vesting date. The first installment vests one year from grant date and the final installment vests five years from grant date. These shares have no expiration date.</footnote>
        <footnote id="F2">The shares reported include 183 shares of restricted stock subject to vesting conditions.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>Kathleen H. Wade under POA for the benefit of Ai-Li Lim</signatureName>
        <signatureDate>2016-01-19</signatureDate>
    </ownerSignature>
</ownershipDocument>
