General manager Jon Daniels said that Martin was to have surgery and would be out from six to eight weeks.
Martin injured the thumb diving into first base to avoid a tag on a bunt play while playing for Triple-A Round Rock. He remained in the game for the inning and was thrown out at third.
Martin, who was batting .347 with three homers and 11 RBIs, was a candidate to be promoted if there was an injury on the Major League club.
"The prognosis is excellent," Daniels said. "It's expected to be six to eight weeks before he's back playing. It shouldn't be something that holds him back, although it's a negative to him."
Larry Millson is a contributor to MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.