The Argentina international opened the scoring in City's 6-3 win against Arsenal on Saturday, but limped out of the clash just five minutes into the second half.
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The busy Christmas period means Aguero could miss as many as eight games, including Liverpool on Boxing Day and their FA Cup third-round clash with Blackburn at the beginning of January.
Aguero should be back to face Barcelona in the Champions League last 16 in the middle of February. The two sides were drawn together on Monday, but Pellegrini is not too concerned by the prospect of facing the four-time winners: "I think Barcelona will be very concerned that they have drawn us. They are not the team of two years ago."
City travel to Leicester in the Capital One Cup quarter-final on Tuesday night, and Pellegrini has also confirmed that Micah Richards and Matija Nastasic will miss out, though Stevan Jovetic is back from injury.
Goal reported on Saturday that City had rejected enquiries from Juventus, AC Milan and Inter for Jovetic, who had been back in full training since the beginning of last week.