The Belgian centre-back suffered the injury in last weekend's 1-0 victory at Stoke City in the fourth round of the FA Cup.
"I hope that he can recover after the FA Cup," Mancini told a news conference, referring to the fifth round match against Leeds United on February 17.
Second-placed City host Liverpool on Sunday in the Premier League by which time they could trail leaders Manchester United by 10 points as Sir Alex Ferguson's side will have already played their game at Fulham on Saturday.
"I think when we arrive at end of February the gap will be very small," he said.
City will have to do their chasing with one striker fewer after this week's departure of Mario Balotelli to AC Milan.
"It will be a problem for you," he told reporters referring to a standing joke that the first questions he normally answered related to Balotelli's on and off-field antics.
"We are not happy because Mario I think he did well. Maybe not in the last three or four months because he had a big problem with injuries, but he did well because Mario helped the team win the Premier League and the FA Cup," Mancini said.
"We thought it was good for everyone, probably, for Mario it could be a big chance to go back to Italy and play in a top club like Milan.
"We hope it will be important for him and for the club that can get back some money."
