Peavy, 29, suffered a detached latissimus dorsi muscle during the second inning of Chicago's 4-1 victory over the Los Angeles Angels on Tuesday, an MRI on Wednesday revealed.
"I knew something was wrong when I walked off the field," Peavy told reporters before Wednesday's game.
Peavy, who won the 2007 Cy Young Award as the National League's best pitcher, is 7-6 with a 4.63 ERA this season but has a 3-2 record and 1.67 ERA over his last six starts.
"You don't want to lose one of your main guys," White Sox pitching coach Don Cooper said on the team's website (http://chicago.whitesox.mlb.com).
"Jake was a great part of what we are doing and what we want to accomplish. But the bottom line is he's gone, and my sights are no longer on him.
"Don't get me wrong. I feel terrible for him, and I know he wants to compete. But he's in a situation where we are going to have to find out more about it and take care of him. That's the long and short of it."
Daniel Hudson, an 11-game winner at Class AAA Charlotte, is expected to take Peavy's spot in the rotation.
(Writing by Steve Ginsburg in Washington; Editing by Greg Stutchbury)