Wright, 7-7 with a 5.94 ERA in 21 starts, aggravated a previous injury Sunday in a start against Tampa Bay, when he left the game in the third inning.
The Indians also designated left-handed reliever Chris Haney for assignment. Haney, who gave up Wade Boggs' 3,000th hit Saturday, has no record and a 3.18 ERA in 11 1-3 innings pitched for the Indians.
Right-hander Jeff Tam, on the roster of Buffalo, Cleveland's affiliate in the International League, also was designated for assignment.
The designation means the Indians have 10 days to trade, release or outright Haney and Tam to the minors.
The Indians activated left-hander Tom Martin from the disabled list. Martin has not pitched for the Indians this season. He had surgery on his left shoulder in January.
The Indians also promoted rookie David Riske from Buffalo. At Akron of the Eastern League, Riske, a right-hander, was 0-0 with a 1.90 ERA and 12 saves. At Buffalo he was 3-0 with an 0.79 ERA and four saves.
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