Exhibit 23.1 Consent of Public Accountant

We consent to the incorporation by reference in the registration statements (No. 333-183481, No. 333-148146, No. 333-117023 and No. 333-171028) on Form S-3 and (No. 333-140152) on Form S-8 of Martin Midstream Partners L.P. of our reports dated March 4, 2013, with respect to the consolidated balance sheets of Martin Midstream Partners L.P. and subsidiaries as of December 31, 2012 and 2011, and the related consolidated statements of operations, comprehensive income, changes in capital, and cash flows for each of the years in the three-year period ended December 31, 2012, and the effectiveness of internal control over financial reporting as of December 31, 2012, which reports appear in the December 31, 2012 annual report on Form 10-K of Martin Midstream Partners L.P.