"There's no serious damage," Rangers manager Ron Washington said. "From a distance, I thought it was his shoulder, but it's his wrist."
Washington said Martin will not be in the lineup on Friday against Toronto southpaw Mark Buehrle, but Martin does not start against left-handed pitchers.
"If I can move my hand, I can play," Martin said through an interpreter.
Martin dealt with an injury in his left hand last season in Triple-A Round Rock, missing five weeks with a torn ulnar collateral ligament in his thumb.
Craig Gentry replaced Martin in center field and hit ninth in the lineup. He struck out swinging during his at-bat in the eighth.
Martin will likely avoid the disabled list, where the Rangers currently have nine players out with injuries. Ian Kinsler made his first rehab assignment in Double-A Frisco on Thursday and went 0-for-4 with two strikeouts. Kinsler is on the 15-day disabled list with a right intercostal strain.
Master Tesfatsionis an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.