The centre-back picked up the injury against Newcastle United on Monday, while Manuel Pellegrini has reiterated that he could sign another defender before the transfer window ends
The centre-back pulled up in the second half of the 4-0 victory over Newcastle United on Monday and had to be substituted.
City boss Manuel Pellegrini has hinted the club could still strengthen before the transfer window closes but will not let the injury to Kompany dictate his transfer activity.
"I prefer the doctor has the final word on this but I think he will be out for at least one month," Pellegrini told reporters..
"If we do strengthen [at centre back] it will not just be because of Vincent Kompany’s injury. We have a very good squad and we see what happens.
"Today or tomorrow we will know exactly how long Vincent will be out for."