City’s top scorer was in tears after leaving the pitch early on during Saturday’s 1-0 Premier League victory at home to Everton.
Pellegrini immediately ruled him out of Wednesday’s crunch Champions League game in Roma, and initial reports suggested Aguero could miss four weeks’ action.
Asked to put a timescale on the Argentine’s absence in a press conference on Tuesday, City’s manager said he expected to be without the player for “four, five, maybe six weeks. It depends a lot on how he recovers. But our team does not depend on one player.”
In an interview with Sports, the City boss then suggested that the striker could miss up to eight weeks, but the recovery period may be shortened if Aguero responds well to treatment.
Aguero has scored 19 goals in 21 games for City this season.