Wright was recalled from Triple-A Norfolk on Friday night. He entered in the fourth inning and got three outs before the injury forced him from the game.
It was Wright's seventh game with Baltimore, the first as a reliever. He's 2-3 with a 4.99 ERA.
The Orioles recalled 26-year-old Jorge Rondon from Norfolk on Saturday to fill Wright's spot in the bullpen.
Rondon went 2-1 with a 2.01 ERA in 24 games with the Tides. He was claimed off waivers by the Orioles from the Colorado Rockies on May 10.