Boston also optioned right-hander Heath Hembree to its top minor league affiliate before Monday night's game against Toronto.
Wright joins the Red Sox for the second time this season after making the opening day roster. The 30-year-old knuckleballer pitched in one game, working the final five innings to earn the win in Boston's 19-inning victory over the New York Yankees on April 10.
The 26-year old Hembree appeared in Sunday's 18-7 loss at Baltimore after being recalled earlier in the day. He gave up six runs while getting only four outs.