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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4/A</documentType>

    <periodOfReport>2014-06-30</periodOfReport>

    <dateOfOriginalSubmission>2014-07-02</dateOfOriginalSubmission>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000831968</issuerCik>
        <issuerName>PROVIDENCE &amp; WORCESTER RAILROAD CO/RI/</issuerName>
        <issuerTradingSymbol>PWX</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001193988</rptOwnerCik>
            <rptOwnerName>ANDERSON RICHARD W</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>75 HAMMOND STREET</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>WORCESTER</rptOwnerCity>
            <rptOwnerState>MA</rptOwnerState>
            <rptOwnerZipCode>01610</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle></officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1340</value>
                    <footnoteId id="F1"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">On July 2, 2014, a Form 4 was filed identifying the incorrect reporting person in Line 1 regarding the purchase of 42 shares of common stock in the Company's Employee Stock Purchase Plan.  As of July 3, 2014 the reporting person owned 1,340 shares of common stock.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Charles D. Rennick on behalf of Richard W. Anderson pursuant to Power of Attorney attached hereto as Exhibit 24.</signatureName>
        <signatureDate>2014-07-03</signatureDate>
    </ownerSignature>
</ownershipDocument>
