Sudfeld injured the shoulder in the first half of Indiana's 45-29 loss at Iowa on Saturday and did not play the rest of the game.
The junior had completed 60.5 percent of his passes for 1,151 yards with six touchdowns and three interceptions in his first year as the undisputed starter for the Hoosiers. He threw for 2,523 yards and 21 touchdowns last season for Indiana while sharing time with Tre Roberson, who transferred in the summer.
True freshman Chris Covington will likely make his first career start at quarterback in Saturday's home game against No. 8 Michigan State.
Covington went 3-for-12 for 31 yards and threw two interceptions while running for 41 yards last week at Iowa.