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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2015-03-16</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000096943</issuerCik>
        <issuerName>TELEFLEX INC</issuerName>
        <issuerTradingSymbol>TFX</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001226614</rptOwnerCik>
            <rptOwnerName>YOH HAROLD L III</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>1500 SPRING GARDEN STREET</rptOwnerStreet1>
            <rptOwnerStreet2>10TH FLOOR</rptOwnerStreet2>
            <rptOwnerCity>PHILADELPHIA</rptOwnerCity>
            <rptOwnerState>PA</rptOwnerState>
            <rptOwnerZipCode>19130</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle></officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2015-03-16</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>128</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>10277</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">Represents additional shares of common stock granted to the reporting person to correct an administrative error in the calculation of the restricted stock award granted to the reporting person on May 2, 2014.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>Daniel V. Logue with POA for Harold L. Yoh III</signatureName>
        <signatureDate>2015-03-18</signatureDate>
    </ownerSignature>
</ownershipDocument>
[{"type": "4", "sequence": "1", "filename": "wf-form4_142672583393671.xml", "description": "FORM 4", "secsgml_size_bytes": 3334}]
X0306
4
2015-03-16
0
0000096943
TELEFLEX INC
TFX
0001226614
YOH HAROLD L III
1500 SPRING GARDEN STREET
10TH FLOOR
PHILADELPHIA
PA
19130
1
0
0
0
Common Stock
2015-03-16
4
A
0
128
A
10277
D
Represents additional shares of common stock granted to the reporting person to correct an administrative error in the calculation of the restricted stock award granted to the reporting person on May 2, 2014.
Daniel V. Logue with POA for Harold L. Yoh III
2015-03-18