Saltalamacchia left Friday night's game against the Boston Red Sox in the fourth inning with the hand problem and was replaced by Taylor Teagarden, who becomes the everyday catcher until Saltalamacchia returns.
The Rangers called up Kevin Richardson from Triple-A Oklahoma City to serve as the backup catcher.
Saltalamacchia was scheduled to be examined by a specialist later on Saturday.
"We've got to figure out what's going on, what's causing it and make sure it's a 15-day thing and be back," Saltalamacchia said. "The more I throw, the more I lose feeling in my arm, get that tingling feeling."
Saltalamacchia said the problem might be nerve-related.
"We're leaning toward some kind of inflammation on that nerve," said Saltalamacchia, batting .236 with nine homers and 34 RBIs in 83 games. "They're hoping rest can knock it out."
The Rangers are in the thick of the AL wild-card race, and they'll miss their No. 1 catcher, who's shown improvement this season on defense and in handling pitchers.
General manager Jon Daniels said the team is happy with Teagarden starting for an extended stretch, but will be monitoring the waiver wire for veteran catchers as trade possibilities.
Teagarden is known more for his defense. He entered Saturday night's start against Boston batting .193 with four homers and 19 RBIs.
"We'll look around to see if there are any players on the market who can help us," Daniels said.
Richardson has been in the Rangers organization since he was signed out of Gonzaga University as a non-drafted free agent in 2002, but has never appeared in the majors.
"I've played for quite a few years now and it's a great feeling to say you finally made it," said Richardson, who hit .223 with 12 homers and 34 RBIs in 66 games for Oklahoma City this season. "It's exciting to be here in the middle of a pennant race."
Max Ramirez likely would have been the Oklahoma City catcher called up by the Rangers, but he just returned from a DL stint due to tendinitis in his left wrist.