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

    <schemaVersion>X0206</schemaVersion>

    <documentType>3</documentType>

    <periodOfReport>2023-03-14</periodOfReport>

    <noSecuritiesOwned>1</noSecuritiesOwned>

    <issuer>
        <issuerCik>0001674416</issuerCik>
        <issuerName>CRISPR Therapeutics AG</issuerName>
        <issuerTradingSymbol>CRSP</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001968317</rptOwnerCik>
            <rptOwnerName>Prasad Raju</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O CRISPR THERAPEUTICS, INC.</rptOwnerStreet1>
            <rptOwnerStreet2>105 WEST FIRST STREET</rptOwnerStreet2>
            <rptOwnerCity>BOSTON</rptOwnerCity>
            <rptOwnerState>MA</rptOwnerState>
            <rptOwnerZipCode>02127</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>Chief Financial Officer</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <footnotes></footnotes>

    <remarks>Exhibit 24 - Power of Attorney
No securities are beneficially owned.</remarks>

    <ownerSignature>
        <signatureName>/s/ Elizabeth Ryland Waldinger</signatureName>
        <signatureDate>2023-03-14</signatureDate>
    </ownerSignature>
</ownershipDocument>
