Exhibit 99.1

Martin Midstream Partners L.P. Announces

Commencement of Public Offering of Common Units

KILGORE, Texas, September 23, 2014 (GlobeNewswire) —Martin Midstream Partners L.P. (Nasdaq: MMLP) (the “Partnership”) announced today that it has commenced an underwritten public offering of 3,000,000 common units (plus up to an additional 450,000 common units pursuant to an option to be granted to the underwriters) under its existing shelf registration statement. The Partnership intends to use the net proceeds from the offering (including any proceeds from the exercise of the underwriters’ option to purchase additional common units) to repay a portion of the outstanding indebtedness incurred under its revolving credit facility and for general partnership purposes. Amounts repaid under the revolving credit facility may be re-borrowed to fund future acquisitions and expansion capital expenditures. BofA Merrill Lynch, RBC Capital Markets, LLC, Wells Fargo Securities, LLC, Deutsche Bank Securities Inc., Goldman, Sachs & Co., Morgan Stanley & Co. LLC, and Raymond James & Associates, Inc. are acting as joint book-running managers for the offering.

The offering is being made by means of a prospectus and related prospectus supplement, copies of which may be obtained from the following addresses:

BofA Merrill Lynch

222 Broadway

New York, NY 10038

Attn: Prospectus Department

Email: dg.prospectus_requests@baml.com

RBC Capital Markets, LLC

Attention: Equity Syndicate

3 World Financial Center

200 Vesey Street, 8^th Floor

New York, NY 10281-8098

Telephone: 877-822-4089

Wells Fargo Securities, LLC

Attention: Equity Syndicate Dept.

375 Park Avenue

New York, NY 10152

Telephone: 800-326-5897

Email: cmclientsupport@wellsfargo.com

Deutsche Bank Securities Inc.

Attn: Prospectus Group

60 Wall Street

New York, NY 10025-2836

Telephone: 800-503-2836

Email: prospectus.cpdg@db.com

Goldman, Sachs & Co.

Attn: Prospectus Department

200 West Street

New York, NY 10282

Telephone: 866-471-2526

Email: prospectus-ny@ny.email.gs.com

Morgan Stanley & Co. LLC

Attention: Prospectus Department

180 Varick Street, 2nd Floor

New York, NY 10014

Raymond James & Associates, Inc.

880 Carillon Parkway

St. Petersburg, Florida 33716

Telephone: 800-248-8863

Email: prospectus@raymondjames.com

Once available, you may also obtain these documents for free by visiting EDGAR on the Securities and Exchange Commission’s website at www.sec.gov.

This press release does not constitute an offer to sell or a solicitation of an offer to buy the securities described herein, nor shall there be any sale of these securities in any state or jurisdiction in which such an offer, solicitation or sale would be unlawful prior to registration or qualification under the securities laws of any such jurisdiction. The offering will be made only by means of a prospectus and related prospectus supplement, which are part of an effective registration statement.

Forward-Looking Statements

Statements in this press release other than historical facts are forward-looking statements within the meaning of the Private Securities Litigation Reform Act of 1995. These forward-looking statements and all references to financial estimates rely on a number of assumptions concerning future events and are subject to a number of uncertainties and other factors, many of which are outside the Partnership’s control, which could cause actual results to differ materially from such statements. While the Partnership believes that the assumptions concerning future events are reasonable, it cautions that there are inherent difficulties in anticipating or predicting certain important factors. A discussion of these factors, including risks and uncertainties, is set forth in the Partnership’s annual and quarterly reports filed from time to time with the Securities and Exchange Commission. The Partnership disclaims any intention or obligation to revise any forward-looking statements, including financial estimates, whether as a result of new information, future events, or otherwise.

About Martin Midstream Partners L.P.

Martin Midstream Partners L.P. is a publicly traded limited partnership with a diverse set of operations focused primarily in the United States Gulf Coast region. The Partnership’s primary business segments include: (1) terminalling, storage and packaging services for petroleum products and by-products; (2) natural gas services, including liquids distribution services and natural gas storage; (3) sulfur and sulfur-based products processing, manufacturing, marketing and distribution; and (4) marine transportation services for petroleum products and by-products.

Joe McCreery,

Vice President – Finance & Head of Investor Relations

Martin Midstream Partners L.P.

Phone: (903) 988-6425

joe.mccreery@martinmlp.com