Cleveland also signed veteran right-hander Jamie Navarro, who is expected to start at Detroit Sunday.
Kane Davis, who debuted in the big leagues June 12 and was scheduled to start Sunday, was optioned to Triple-A Buffalo. Cleveland also designated left-hander Mark Watson for assignment.
In addition, the Indians sent right-hander Willie Martinez back to Buffalo and purchased the contract of reliever Brian Williams from their Triple-A club to replace him.
They also signed left-hander Mike Mohler to a minor league contract. Mohler, 31, appeared in 22 games for St. Louis this season but had a 9.00 ERA and was released by the Cardinals June 5.
Wright received a second opinion on his injured right shoulder this week from Anaheim Angels team orthopedist Dr. Lewis Yocum. Yocum's diagnosis was the same as that of Indians physician Dr. Louis Keppler, who prescribed that Wright rest his arm for two weeks, then begin a light throwing program.
Wright was 3-4 with a 4.70 ERA when his inflamed shoulder forced him on the DL.
Navarro has a major league record of 116-125 in 12 seasons with Milwaukee, the Chicago White Sox and Chicago Cubs. He started the season with the Brewers but went 0-5 with a 12.54 ERA and was released. Navarro was signed to a minor league contract with the Colorado Rockies and was 3-2 with a 5.30 ERA for Triple-A Colorado Springs.
Williams, released by the Cubs May 25 after going 1-1 with a 9.62 ERA in 22 appearances, was 1-0 with a 2.08 ERA in three games for Buffalo.
Martinez made his major league debut in Cleveland's 11-4 loss to Chicago Wednesday night and pitched three solid innings.