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 February 18 with the return leg at the Nou Camp on March 12.
"The injuries are Samir Nasri, Javi Garcia and Sergio Aguero," Pellegrini told reporters. "The doctor has seen Aguero and he will be out for a month.
"It will be difficult because he is a top player for us but we have the players to replace him. He has just come back from injury. Alvaro Negredo and Edin Dzeko replaced him then and Stevan Jovetic can now."
Free-scoring Premier League leaders City host third-placed Chelsea on Monday having won eight successive league games since drawing at Southampton in early December.
They have scored 42 goals in 11 league wins at the Etihad this season and a remarkable 115 in all competitions home and away.
Their emphatic victory at Spurs led the London side's manager Tim Sherwood to describe Pellegrini's team as "the best team on the planet" but the Chilean dismissed such talk.
"I don't think we are the best team in the planet," he said. "But if we play exactly the way we did against Tottenham, we are a very good team.
"At the moment, we are not thinking about titles. We are thinking about improving and winning every game."
City head the standings by a point from Arsenal with Chelsea three points behind the leaders and Pellegrini said there would be plenty of twists and turns in the title race.
"Arsenal and Chelsea are both having a good season. Just because they have dropped points does not mean they are weaker.
"Whatever happens in the game, the season is not over. There are still 42 points to play for.
(Reporting by Steve Tongue and Justin Palmer, editing by Ed Osmond) nL3N0L553E
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