The 21-year-old sustained the injury during the first meeting between the two nations at Carrow Road on Friday evening.
Despite admitting that Rodwell's exclusion is a blow, manager Stuart Pearce is confident that they will cope with the City player's absence.
"We're disappointed for Jack, naturally, but I know what I've got in this squad and I know they're good enough to see the job through," said Pearce.
"We've had a lot of injuries to contend with throughout this qualification campaign so it's not a challenge we're unfamiliar with. I know my players and I'm no less confident in our chances."
Rodwell has now returned to City for further treatment.