The influential centre-back has not featured since suffering a thigh injury in the victory over Everton last month.
He will play no part in City's Premier League game against Norwich on Saturday or the trip to Sunderland the following weekend.
Javi Garcia and Stevan Jovetic have also been ruled out of the game against Norwich after picking up injuries in the League Cup win at Newcastle in midweek.
"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 said.
"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.
"In the last five matches we have won four and we lost just one against Chelsea, but I think we deserved more."