Wright pitched in two games out of the bullpen with Baltimore before going on the 15-day DL on April 11 with a left trapezius strain. He was transferred to the 60-day disabled list May 24.
The 30-year-old Wright finished his rehabilitation assignment Sunday, and the Orioles cut ties with him Wednesday.
Baltimore has 10 days to either trade Wright or release him. He could also accept a minor league assignment with the team.
Since breaking into the majors in 2008 with Houston, Wright is 10-18 with a 4.18 ERA. He signed as a free agent with Baltimore in December after pitching last season for the Chicago Cubs.