Exhibit 32.1

CERTIFICATION PURSUANT TO 18 U.S.C.  SECTION 1350,

AS ADOPTED PURSUANT TO SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002*

In connection with the Quarterly Report of Martin Midstream Partners L.P., a Delaware limited partnership (the “Partnership”), on Form 10-Q for the quarter ended September 30, 2016, as filed with the Securities and Exchange Commission (the “Report”), I, Ruben S. Martin, Chief Executive Officer of Martin Midstream GP LLC, the general partner of the Partnership, certify, pursuant to Section 906 of the Sarbanes-Oxley Act of 2002 (18 U.S.C. Section 1350), that to my knowledge:

(1)          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 Partnership.

/s/ Ruben S. Martin

Ruben S. Martin,

Chief Executive Officer

of Martin Midstream GP LLC,

the General Partner of Martin Midstream Partners L.P.

October 26, 2016

*A signed original of this written statement required by Section 906 has been provided to the Partnership and will be retained by the Partnership and furnished to the Securities and Exchange Commission or its staff upon request.