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

    <schemaVersion>X0206</schemaVersion>

    <documentType>3</documentType>

    <periodOfReport>2016-01-08</periodOfReport>

    <noSecuritiesOwned>0</noSecuritiesOwned>

    <issuer>
        <issuerCik>0000876167</issuerCik>
        <issuerName>PROGRESS SOFTWARE CORP /MA</issuerName>
        <issuerTradingSymbol>PRGS</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001320769</rptOwnerCik>
            <rptOwnerName>Praesidium Investment Management Company, LLC</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>1411 BROADWAY - 29TH FLOOR</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10018</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle></officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001662082</rptOwnerCik>
            <rptOwnerName>Oram Kevin</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>1411 BROADWAY - 29TH FLOOR</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10018</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle></officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001662083</rptOwnerCik>
            <rptOwnerName>Uddo Peter</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>1411 BROADWAY - 29TH FLOOR</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10018</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle></officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>6786324</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                    <footnoteId id="F3"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnotes</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                    <footnoteId id="F3"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">On January 8, 2016, Praesidium Investment Management Company, LLC (&quot;Praesidium&quot;) in a single transaction purchased 1,800,000 shares of common stock (the &quot;Purchased Shares&quot;) of Progress Software Corporation (the &quot;Issuer&quot;) on behalf of certain third party accounts it manages (the &quot;Managed Accounts&quot;) and certain investment fund vehicles (the &quot;Investment Fund Vehicles&quot;) for which Praesidium serves as investment manager.  Purchased Shares were allocated to the Managed Accounts and Investment Fund Vehicles.  Praesidium may be deemed to beneficially own 6,442,910 shares of common stock of the Issuer held in the Managed Accounts (the &quot;Managed Account Shares&quot;) and 343,414 shares of common stock of the Issuer held in the accounts of the Investment Fund Vehicles (the &quot;Investment Fund Vehicle Shares&quot;) because Praesidium may be deemed to exercise investment power over such shares.</footnote>
        <footnote id="F2">(Cont' from Footnote 1): Kevin Oram and Peter Uddo may be deemed to beneficially own the Managed Account Shares and the Investment Fund Vehicle Shares because they may be deemed to control Praesidium as the managing members of Praesidium.  Praesidium, Mr. Oram and Mr. Uddo may be deemed to have a pecuniary interest in the Managed Account Shares due to Praesidium's right to receive performance fees subject to certain hurdles or benchmarks.  Further, Praesidium, Mr. Oram and Mr. Uddo may be deemed to have a pecuniary interest in the Investment Fund Vehicle Shares due to their indirect right to receive a performance fee and/or performance allocation, as applicable, subject to certain hurdles or benchmarks.</footnote>
        <footnote id="F3">(Cont' from Footnote 2): Each of Praesidium, Mr. Oram and Mr. Uddo disclaims beneficial ownership of the reported securities of the Issuer except to the extent of his or its pecuniary interest therein, and this report shall not be deemed an admission that any of Praesidum, Mr. Oram or Mr. Uddo is the beneficial owner of such securities for Section 16 or any other purpose.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>Praesidium Investment Management Company, LLC by /s/ Kevin Oram, Managing Member</signatureName>
        <signatureDate>2016-01-11</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ Kevin Oram</signatureName>
        <signatureDate>2016-01-11</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ Peter Uddo</signatureName>
        <signatureDate>2016-01-11</signatureDate>
    </ownerSignature>
</ownershipDocument>
