Tests suggest that his ligaments have been torn, which will rule him out for the rest of the campaign.
City have no natural anchorman to replace him, with midfielder Richie Appleby and utility player Damien Delaney previously filling in for him.
Meanwhile, Marc Joseph hopes to be fit to play in City's next game at Rushden & Diamonds on Saturday. He limped out of the Oxford game with an ankle injury, but should have recovered by the end of the week.