The Frenchman picked up the problem during training in the week and will miss the trip to face his former club Arsenal on Sunday, live on Sports.
City manager Manuel Pellegrini said of the 27-year-old: “We have had some problems during the week with Samir.
“I think he will be out for three weeks but to come back before then will be very difficult.”
Better news for the reigning Premier League champions comes in the forms of Sergio Aguero and Vincent Kompany, who are both pushing for recalls at Emirates Stadium in the wake of injuries.
Pellegrini said of the influential pair: “Vincent is 100% okay, no problems.??Sergio is working with the squad every day, so he doesn’t have any problem. We will see if he starts, but at the moment he is 100 per cent fit.”