The injury occurred earlier today when City trained in Ukraine ahead of tomorrow's Champions League match against Shakhtar Donetsk.
The setback is inconvenient for the Manchester club who already have Aymeric Laporte midfielder on the injury list, who are not expected to return until January or February.
This means that they have only one clean center back injury-free, Nicolas Otamendi. In addition, they have a packed schedule with the Premier League, Champions League and the League Cup. In the worst case, he could miss eight matches in the league and cup games, for a team that surprisingly lost this weekend's Premier League match against Norwich by 3-2.