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

    <schemaVersion>X0204</schemaVersion>

    <documentType>3</documentType>

    <periodOfReport>2012-02-16</periodOfReport>

    <noSecuritiesOwned>0</noSecuritiesOwned>

    <issuer>
        <issuerCik>0001324503</issuerCik>
        <issuerName>Patni Computer Systems LTD</issuerName>
        <issuerTradingSymbol>PTI</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0000937611</rptOwnerCik>
            <rptOwnerName>ELLIOTT INTERNATIONAL, L.P.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O MAPLES &amp; CALDER, P.O. BOX 309</rptOwnerStreet1>
            <rptOwnerStreet2>UGLAND HOUSE, SOUTH CHURCH STREET</rptOwnerStreet2>
            <rptOwnerCity>GEORGE TOWN</rptOwnerCity>
            <rptOwnerState>E9</rptOwnerState>
            <rptOwnerZipCode>00000</rptOwnerZipCode>
            <rptOwnerStateDescription>CAYMAN ISLANDS</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>Ordinary Shares</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>8852404</value>
                    <footnoteId id="F1"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">The 8,852,404 Ordinary Shares reported on this Form 3 consist of: (a) 8,845,320 Ordinary Shares owned by Elliott International, L.P. (&quot;Elliott International&quot;) through Suffolk (Mauritius) Limited, a Mauritius company and wholly-owned subsidiary of Elliott International, and (b) 3,542 American Depositary Shares owned directly by Elliott International, representing 7,084 Ordinary Shares.  Each American Depositary Share represents two Ordinary Shares.</footnote>
        <footnote id="F2">Elliott International Capital Advisors Inc., a Delaware corporation (&quot;EICA&quot;), is the investment manager of Elliott International.  EICA may be deemed to have beneficial ownership of the securities owned by Elliott International.  EICA disclaims any pecuniary interest in any of the securities with respect to which indirect beneficial ownership is described in this Form 3.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>Elliot Greenberg, V.P. of Elliott International Capital Advisors Inc., as Attorney-In-Fact for Elliott International, L.P.</signatureName>
        <signatureDate>2012-02-22</signatureDate>
    </ownerSignature>
</ownershipDocument>
