One of their replacements, reliever Joakim Soria, is poised for his first major league appearance in nearly two years.
Berkman, a 37-year-old with a history of knee trouble, suffered an injury to his hip or lower back running to first base in Saturday's 9-5 loss to Houston. He stayed in the game for one more at-bat before leaving in the seventh inning.
"It's kind of hard to tell if it is a high glut or the lower back," Berkman said. "It feels terrible. But the day after is always bad.
The injury came about a week after Berkman tweaked his right knee when he took a wrong step getting off a plane and missed four games.
"Give him a chance to catch up with his knee, and his knees causing other things to flare up and putting a band aid on this and putting a band aid on that," Rangers manager Ron Washington said. "We just felt like we needed to give him some time so he can be productive for us."
Berkman played just 32 games last year with St. Louis because of two operations on his right knee and a left calf strain. He was considering retirement when the Rangers offered a one-year, $11 million deal.
He was hitting .311 on May 19, but has slumped to .185 over his past 29 games.
"When we signed him, we thought everything was going to be fine with the knees," Washington said. "And the knees really haven't been an issue. We feel strongly that when he comes back, he'll have all this behind him."
"It's definitely frustrating," added Berkman, a career .294 hitter with 366 home runs. "I feel bad just not to be able to go out there and do my job."
Tepesch went to the DL with right elbow inflammation two days after getting the win in a 10-5 victory against the Astros. He threw five shutout innings, but his night ended after the first four hitters reached in the sixth.
The 24-year-old was playing catch Saturday when he said his elbow was sore, and Washington said the move was precautionary.
Soria, a two-time All-Star with Kansas City, hasn't pitched in the majors since Sept. 11, 2011, with the Royals. The right-hander was recovering from elbow reconstruction surgery when he strained his right pectoral muscle while rehabbing in Arizona in late April.
The 29-year-old Soria was reinstated from the 60-day DL after seven shutout innings in seven rehab starts.
The Rangers also called up right-handed reliever Cory Burns from Triple-A Round Rock. Burns made three appearances during a weeklong stint with Texas in May, giving up two runs in 3 2-3 innings. He has a 1.05 ERA in 26 games with Round Rock.
ESPNDallas.com's Randy Jennings and The Associated Press contributed to this report.