The 29-year-old righty has not pitched in the majors since June 2007 because of shoulder trouble.
"We are disappointed that Henry Owens received a positive test, and fully endorse the discipline outlined in the MLB policy," Marlins president of baseball operations Larry Beinfest said in a statement. "We will continue to work with and educate our players to help prevent any further violations."
Owens made three relief appearances for the Marlins in 2006. He pitched 22 times in 2007, going 2-0 with four saves and briefly becoming the team's closer.
He injured his right shoulder that year and was on the disabled list from May 9 until June 1. When he returned, he made just five appearances, went back on the DL and then had shoulder surgery on Aug. 30.
Owens was just the third player this year suspended under the major league drug program, following Humberto Cota and Eliezer Alfonzo. There were 66 suspensions under the minor league program, including 40 from the Dominican Summer League and 10 from the Venezuelan Summer League.
Owens' agent, Greg Genske, did not return a message seeking comment.