Speight was injured against Purdue on Sept. 23, but the details of the injury haven't been made public. The Wolverines were on a bye last week, and Harbaugh had previously said if they did have a game that Speight would not have been able to play.
"He won't be able to compete this week or for multiple weeks," Harbaugh said Monday
O'Korn took over in the first quarter against Purdue and went 18-for-26 passing for 270 yards with one touchdown and one interception in a 28-10 win after the Wolverines trailed 10-7 at halftime.
"John's done a fantastic job ever since he got here in every role that he's been in," Harbaugh said. "He's acquitted himself well, including coming off the bench and leading our team to victory against Purdue. I think that speaks volumes."
Coming into Saturday's game, Michigan's offense ranks 73rd in the FBS in total yards per game and 72nd in passing yards per game. O'Korn's sample size is smaller than Speight's, but he has completed 70.4 percent of his pass attempts and has thrown for 11.4 yards per attempt.
The Associated Press contributed to this report.