Aguero limped off in City’s thumping of Spurs in midweek and will now miss crucial games in the Premier League, Champions League and FA Cup.
City face Chelsea in the league on Monday night and in the FA Cup later on this month as well as Barcelona in the Champions League.
The Argentinean hitman, who has 26 goals already this season, will be back for the Capital One Cup final against Sunderland and the second leg of their Champions League clash with Barcelona.
Edin Dzeko and Stevan Jovetic are to battle for Aguero’s spot in the team as City did not bring in a striker in the transfer window.
“It is very difficult. Sergio is a top player for us but I think we can replace him,” boss Manuel Pellegrini said.
“As with the other injury, we hope we can continue to do it. But, of course, he is a very important player for us.
“Sergio is just coming back from an injury – one month that he couldn’t play.