Pence suffered the injury in Sunday's 11-3 loss to the Cincinnati Reds. He is eligible to return from the injured list June 27.
The Rangers recalled outfielder Willie Calhoun from Triple-A Nashville in a corresponding move. Calhoun suffered a strained left quad muscle on May 22 and was 3-for-11 with two walks on his medical rehab assignment.
Pence is hitting .294 with 15 home runs and 48 RBIs in 55 games this season. He is second in the American League All-Star voting at designated hitter.
The three-time All-Star is a career .280 hitter with 239 home runs. His 15 home runs this season are already his most since hitting 20 for the San Francisco Giants in 2014.
Texas is 39-33 this season. The Rangers and Boston Red Sox are tied for second in the American League Wild Card standings.