The Cubs recalled right-hander Blake Parker from Triple-A Iowa before Tuesday night's game at San Francisco to take Wright's place.
Wright is 0-1 with a 3.18 ERA this season. He has struck out 14 and walked six in 17 innings.
Parker made two appearances for the Cubs earlier this season, allowing three runs in 1 2-3 innings. He has a 0.77 ERA with 15 strikeouts and no walks in 11 2-3 innings for Iowa.