David Luiz suffered a small fracture in his wrist during Chelsea's draw with Arsenal on Sunday.
The Brazilian, who was sent off for a challenge on Sead Kolasinac, collided with the hoardings and is now wearing a splint to support the injury.
Luiz will miss the next three games through suspension, which includes the trip to Manchester to face Pep Guardiola's City.
The 30-year-old is expected to recover from the injury after the international break and should be available for Chelsea's visit to Crystal Palace on October 14.