The Manchester City striker picked up a calf muscle in Saturday's thrashing of Arsenal and could miss as many as eight games given the hectic Christmas schedule.
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.
"Sergio has a calf injury," Pellegrini told reporters. "The doctor can say how many weeks he will be out. I don't know at the moment. I think he will be out for at least one month."
The busy Christmas period means Aguero could miss as many as eight games, including Liverpool on Boxing Day and an 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 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 travels to Leicester for a Capital One Cup quarterfinal on Tuesday, and Pellegrini has also confirmed that Micah Richards and Matija Nastasic will miss out, though Stevan Jovetic is back from injury.