Gallo, 25, suffered the injury in Saturday's 6-2 victory over the Kansas City Royals. He first reported the injury after trying to make a throw from the outfield in the fifth inning.
Gallo left the game midway through his at-bat in the bottom of the fifth inning.
The Rangers recalled outfielder Delino DeShields from Triple-A Nashville in a corresponding move.
Gallo is hitting .276 with 17 home runs and 41 RBIs in 170 at-bats this year. The veteran outfielder is on pace to finish with a batting average above .209 for the first time in his career.
Texas entered play Sunday with a 29-27 record. The Rangers are 8 1/2 games behind the Houston Astros for first place in the AL West Division.