An MRI showed he could be out four to six weeks.
"I've never had it happen. (The doctor) told me the same thing y'all have heard: four weeks," Moreland said. "I'm going to do my treatment, try to prepare the best I can, get back healthy and get ready to go as quick as I can."
Roy Oswalt replaces Moreland on the 25-man roster. The Rangers designated pitcher Mark Hamburger for assignment to make room on the 40-man roster for Oswalt.
Moreland suffered the injury trying to beat out a double-play ball in Tuesday's 7-3 win in San Diego.
Moreland, 26, is hitting .272 with 10 homers and 25 RBIs. He batted just .231 in April but hit the ball much better in May to raise his average.