Speight was injured in the first quarter of the Wolverines' most recent game, Sept. 23 against Purdue. O'Korn replaced Speight and finished the 28-10 victory, completing 18 of 26 passes for 270 yards, with one touchdown and one interception.
Harbaugh did not disclose the nature of Speight's injury.
Speight has completed 44 of 81 passes for 581 yards, with three touchdowns and two interceptions.
O'Korn started 16 games at Houston before his transfer to Michigan. He will be making his second career start for the Wolverines.
Sophomore Brandon Peters will be the backup quarterback when Michigan hosts rival Michigan State on Saturday.