The centre back, sidelined since picking up the problem in his team's opening league game of the season against Newcastle United last month, is one of five players to be ruled out of the trip to former City boss Mark Hughes's Stoke.
Attacking midfielder David Silva, who has a thigh injury that cut short his time on Spain duty this week, is also among the absentees and could be a doubt for Tuesday's Champions League match at Viktoria Plzen.
Martin Demichelis is out of action for several more weeks with a knee injury and fellow defenders Micah Richards and Gael Clichy will not be fit to play this weekend.
"Kompany is OK but it's a risk for him to play this match (at Stoke) - two or three more days and he will be 100 percent," coach Manuel Pellegrini told a news conference on Friday.
The dependable Belgium international will be returning at just the right time as City's European game is closely followed by a home match against Premier League champions Manchester United on Sept. 22.
"It's a big test for all of the big clubs, all of them are playing the Champions League and Europa League - we have seven games in 21 days," the Chilean said.
Stoke manager Hughes has no injury problems with Kenwyne Jones, Glenn Whelan and Jonathan Walters having recovered from knocks picked up on international duty.
He could hand debuts to Marko Arnautovic, signed on transfer deadline day from Werder Bremen, and Stephen Ireland, on loan from Aston Villa, against the club he managed between 2008 and 2009.
"Marko has come in over the last 48 hours and looked very sharp and technically very impressive too, so he along with Stephen comes into my thoughts for the game," Hughes said on the club website (www.stokecityfc.com).
Manchester City, who have won two and lost one of their first three matches of the season, do not have a brilliant recent record at the Britannia Stadium with their last four league games having ended in 1-1 draws.
"They're a very good team at home, they have a good approach in the box - like every other game, we'll have to do very well if we want to win," Pellegrini said.