The Belgium defender underwent a scan in Manchester on Monday after suffering the groin injury during the first 34 minutes of City's 3-1 win over Everton in the Premier League on Saturday.
Kompany missed three Premier League matches with a groin injury before returning to the squad for the Champions League game against Viktoria Plzen.
He has played four matches since, including the game against Everton.
Kompany had complained of feeling pain 24 hours after the match against Everton leading to fear he had strained the muscle.
He will miss Belgium's World Cup qualifiers with Croatia on Friday and Wales next Tuesday.
Benteke picked up a hip injury in Aston Villa's 1-0 victory at Norwich on Sept. 21. Villa initially said he would be out for at least four weeks.
Belgium top Group A with a five-point advantage over second placed Croatia and a draw in Zagreb would mean they reach their first finals in 12 years.
Even if they lose to Croatia, Belgium would still ensure their ticket to Brazil in 2014 with victory in their last match against Wales.