Marte, who was put on the 15-day disabled list on May 3, went to see Andrews in Birmingham, Ala., after team doctors diagnosed him with weakness and tendinitis in his pitching shoulder.
New York announced that Andrews concurred with previous evaluations made by Yankees team physician Dr. Christopher Ahmad as well as Dr. David Altchek.
"They're not telling him to have surgery, so they're telling him that they believe he can get back," Yankees manager Joe Girardi said. "That leads me to believe that he can get back. It's frustrating, because we'd love to have him and we need him. It's great to have two lefties in your bullpen."
The 34-year-old left-hander had pitched only 5 1/3 innings for New York this season, giving up nine runs for a 15.19 ERA. Throughout his 10-year career, Marte owns a 3.43 ERA as mostly a setup man.
Marte, who signed a three-year, $12 million contract this offseason, complained of shoulder soreness while pitching for the Dominican Republic in the World Baseball Classic this spring.
Bryan Hoch is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.