The Red Sox will need to call up a starting pitcher for Thursday's game to replace Wright in the rotation.
The last time Boston needed a starter, left-hander Brian Johnson got the call from Pawtucket and earned a win on April 18 in Toronto.
Johnson last pitched at Triple-A on April 27, so he could be an option again.
Wright is off to a tough start this season, going 1-3 with an 8.25 ERA in five starts.
He last pitched on Saturday against the Cubs, taking the loss.
When did the knee injury crop up?
"It was [Sunday] that he felt it more than anything," said Red Sox manager John Farrell. "He didn't feel it during his outing against the Cubs. This is somewhat of an ailment in the knee he's been feeling on and off since Spring Training, but to the extent of this, this really crept up yesterday."
Left-hander David Price has been on the disabled list since the start of the season with a left elbow strain and there is no timetable for his return to action.
Ian Browne has covered the Red Sox for MLB.com since 2002. Follow him on Twitter @IanMBrowne and Facebook. This story was not subject to the approval of Major League Baseball or its clubs.