He will now miss key games against Chelsea in both the Premier League and FA Cup and at least one leg of the Champions League tie against Barcelona.
The Spanish side are due in Manchester on February18 with the return leg at the Nou Camp on March 12.
"Sergio is a top player for us but I think we can replace him," Pellegrini told reporters. "All the other strikers, Alvaro Negredo, Edin Dzeko and Stefan Jovetic replace him."
(Reporting by Steve Tounge, editing by Mike Collett)