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.
Mancini was undaunted and reckoned that by the end of this month his club will have closed in on the leaders.
"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.
Mancini thought that three strikers - Carlos Tevez, Edin Dzeko and Sergio Aguero - would be enough for the job since they had only the league and cup to concentrate on after failing to progress in European competition.
Almost of more concern was what questions Mancini would now face at his Friday news conferences without the fiery Balotelli to discuss.
"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.
He hoped it would be a good move for the 22-year-old Italian striker and that despite an up-and-down relationship he was sad to see him go.
"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."
