The centre-back sustained a calf problem and was absent from training with his national team on Wednesday, putting his participation in Thursday's friendly against Australia in doubt.
Kompany is being assessed and Belgium's medical team are awaiting results of a scan before they can determine the extent of the injury.
"No @vincentkompany at training today," Belgium coach Marc Wilmots wrote on Twitter.
"He was taken to the hospital for a calf scan
We'll have to wait for the results."
Anything longer than a week on the sidelines for Kompany would give City manager Manuel Pellegrini a problem.
On their resumption after the international break City face, in the space of eight days, Arsenal and Chelsea in the Premier League either side of trip to Bayern Munich in the Champions League.
City's £32million summer signing Eliaquim Mangala has yet to feature in a match-day squad since the centre-back's arrival from Porto in mid-August while last season's back-up Matija Nastasic has not made a squad since playing 90 minutes in the Community Shield defeat to Arsenal.
Source : PA
Source: PA