CERTIFICATION PURSUANT TO RULE 30A-2(B) UNDER THE 1940 ACT AND SECTION 906 OF
                             THE SARBANES-OXLEY ACT

I, James M. Dykas, Chairman of the Board, President and Chief Executive Officer
of First Trust Exchange-Traded Fund (the "Registrant"), certify that:

      1.    The Form N-CSR of the Registrant (the "Report") fully complies with
            the requirements of Section 13(a) or 15(d) of the Securities
            Exchange Act of 1934, as amended; and

      2.    The information contained in the Report fairly presents, in all
            material respects, the financial condition and results of operations
            of the Registrant.

Date: September 6, 2019                /s/ James M. Dykas
     -------------------               ----------------------------------------
                                       James M. Dykas, President and
                                       Chief Executive Officer
                                       (principal executive officer)


I, Donald P. Swade, Treasurer, Chief Financial Officer and Chief Accounting
Officer of First Trust Exchange-Traded Fund (the "Registrant"), certify that:

      1.    The Form N-CSR of the Registrant (the "Report") fully complies with
            the requirements of Section 13(a) or 15(d) of the Securities
            Exchange Act of 1934, as amended; and

      2.    The information contained in the Report fairly presents, in all
            material respects, the financial condition and results of operations
            of the Registrant.

Date: September 6, 2019                /s/ Donald P. Swade
     -------------------               ----------------------------------------
                                       Donald P. Swade, Treasurer,
                                       Chief Financial Officer and
                                       Chief Accounting Officer
                                       (principal financial officer)