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

    <schemaVersion>X0206</schemaVersion>

    <documentType>3</documentType>

    <periodOfReport>2012-12-14</periodOfReport>

    <noSecuritiesOwned>0</noSecuritiesOwned>

    <issuer>
        <issuerCik>0001362925</issuerCik>
        <issuerName>Planet Payment Inc</issuerName>
        <issuerTradingSymbol>PLPM</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001342335</rptOwnerCik>
            <rptOwnerName>Cox Robert J III</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O PLANET PAYMENT, INC.</rptOwnerStreet1>
            <rptOwnerStreet2>670 LONG BEACH BOULEVARD</rptOwnerStreet2>
            <rptOwnerCity>LONG BEACH</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>11561</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>SVP, CFO and Treasurer</officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>100000</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeHolding>
            <securityTitle>
                <value>Stock Option (Right to Buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>1.65</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <footnoteId id="F1"/>
                <footnoteId id="F5"/>
            </exerciseDate>
            <expirationDate>
                <value>2019-11-29</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>200000</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
        <derivativeHolding>
            <securityTitle>
                <value>Stock Option (Right to Buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>1.24</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <footnoteId id="F2"/>
                <footnoteId id="F5"/>
            </exerciseDate>
            <expirationDate>
                <value>2020-11-29</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>100000</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
        <derivativeHolding>
            <securityTitle>
                <value>Stock Option (Right to Buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>2.00</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <footnoteId id="F3"/>
                <footnoteId id="F5"/>
            </exerciseDate>
            <expirationDate>
                <value>2021-04-11</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>100000</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
        <derivativeHolding>
            <securityTitle>
                <value>Stock Option (Right to Buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>2.8</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <footnoteId id="F4"/>
                <footnoteId id="F5"/>
            </exerciseDate>
            <expirationDate>
                <value>2022-04-01</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>65000</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">This is a stock option grant under the Issuer's 2006 Equity Incentive Plan (the &quot;Plan&quot;).  Vesting at the rate of one-third (1/3rd) of the total number of shares annually, this grant is fully vested and exercisable as of the date of this filing, provided the Reporting Person continues to provide services to the Issuer.  None of these shares has been exercised by the Reporting Person to date.</footnote>
        <footnote id="F2">This is a stock option grant under the Plan and will be vested and exercisable as follows: one-third (1/3rd) of the total number of shares annually starting November 30, 2010, such that the grant vests in full after three years, provided the Reporting Person continues to provide services to the Issuer.  None of these shares has been exercised by the Reporting Person to date.</footnote>
        <footnote id="F3">This is a stock option grant under the Plan and will be vested and exercisable as follows: one-third (1/3rd) of the total number of shares annually starting November 30, 2011, such that the grant vests in full after three years, provided the Reporting Person continues to provide services to the Issuer.  None of these shares has been exercised by the Reporting Person to date.</footnote>
        <footnote id="F4">This is a stock option grant under the Plan and will be vested and exercisable as follows: one-third (1/3rd) of the total number of shares annually starting January 1, 2012, such that the grant vests in full after three years, provided the Reporting Person continues to provide services to the Issuer.  None of these shares has been exercised by the Reporting Person to date.</footnote>
        <footnote id="F5">Vesting of this stock option grant will be accelerated in full in the event of a termination upon a change of control or an involuntary termination of the Reporting Person, as provided in the executive retention agreement between the Reporting Person and the Issuer.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/  Graham N. Arad, as attorney-in-fact</signatureName>
        <signatureDate>2012-12-14</signatureDate>
    </ownerSignature>
</ownershipDocument>
