Green sustained the injury in the third quarter of last Saturday's season-opening loss at Stanford. Fitzgerald said after the game that Green had been taken to a local hospital and would need surgery.
Green, the son of former NFL quarterback Trent Green, served as Northwestern's backup quarterback the past two seasons and appeared in nine games in 2018.
He and Clemson transfer Johnson competed for the starting job throughout the offseason, with Johnson getting the start against Stanford. Green had 62 passing yards and 10 rushing yards in the 17-7 loss.
A fifth-year senior, Green could apply for a sixth-year hardship waiver because the injury occurred in the opener.
Northwestern starting running back Isaiah Bowser, who sustained a knee injury against Stanford, was running around at practice Thursday, Fitzgerald said. The team is off this week before hosting UNLV on Sept. 14.