The City skipper will miss his side's games against Norwich and Sunderland as they attempt to climb the table.
Pellegrini's side have struggled in the Belgians absence, with a defensive mix-up costing them late on against Chelsea in their last league game.
Kompany picked up the injury last month in a 3-1 win over Everton, and the news that he will miss further games will come as a blow to City.
Javi Garcia - who has looked shaky when placed at centre-half - is also out for City's game at the weekend, along with summer signing Stevan Jovetic.
"Garcia and Jovetic have a problem from the last match and Vincent Kompany is not fit. All the other players are okay," the former Malaga boss is quoted as saying on fourfourtwo.com.
"Garcia does not have a serious injury, but he will be out tomorrow (Saturday). Vincent is progressing. I think he will be back after the international break, but not before.
"He is a very important player, but we have a strong squad and the other players can play. He is an important player but we can play without him.
Pellegrini will be unhappy with his side's start to the Premier League as the 2012 champions linger in seventh.
A win at the weekend could elevate the Citizens into the top four should results go their way.
Following a number of high-profile blunders it appears the Chilean may finally be losing patience with Joe Hart.
Reports have emerged that the England international will be dropped for this weekend's fixture and replaced by Costel Pantilimon.