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

I, James M. Dykas, 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: March 11, 2019                    /s/ James M. Dykas
     ----------------                   ----------------------------------------
                                        James M. Dykas, President and.
                                        Chief Executive Officer
                                        (principal executive officer)


I, James M. Dykas, 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: March 11, 2019                    /s/ Donald P. Swade
     ----------------                   ----------------------------------------
                                        Donald P. Swade, Treasurer,
                                        Chief Financial Officer and
                                        Chief Accounting Officer
                                        (principal financial officer)