The England defender picked up the injury before United suffered their first league defeat of the season in going down 2-1 at Wolves last weekend.
The United skipper is not expected to return until the end of February at the earliest.
United are five points ahead of City having played a game less.
They will bolster their title hopes considerably with a win, but could also be without Darren Fletcher, who withdrew from Scotland's match with Northern Ireland on Wednesday due to an ankle knock.
City are without Adam Johnson with an ankle injury, while there ar doubts over Mario Balotelli, Micah Richards and Nigel de Jong.
Arsenal manager Arsene Wenger could be without 11 players against Wolves due to various injurie.
Abou Diaby is suspended for the visit of the league's bottom club after being sent off for pushing Joey Barton in last Saturday's 4-4 draw with Newcastle.
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