Wright experienced discomfort in his shoulder Friday while pitching against Toronto. He didn't feel better Saturday, so he has been put on the DL with a strained trapezius.
It is Wright's first stint on the disabled list since 2009, when he strained his left shoulder with the Astros.
The 30-year-old Wright was signed to a one-year contract in December after playing with the Cubs in 2014.
Baltimore filled the void by recalling right-hander Eddie Gamboa from Triple-A Norfolk.
Gamboa's visit could be a short one. The Orioles will need a roster spot for outfielder David Lough, who is expected to be activated from the disabled list in a few days.