The Belgium international sustained the injury after contesting a challenge with Stoke striker Kenwyne Jones.
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The City skipper hobbled off the pitch in the 33rd minute and proceeded to walk straight down the tunnel.
The injury could be a massive blow to Roberto Mancini's side as they face crucial Premier League clashes with Liverpool and Chelsea in the coming weeks, and could be without their inspirational leader.
There was clear confusion following Kompany's injury as David Platt and Mancini deliberated for a number of minutes before finally deciding to bring on Gael Clichy, switching to three at the back.
Platt revealed after the match that the defender will definitely miss their next game against QPR on Tuesday.
"He's pulled his calf," he revealed.
"We won't know how bad it is until the morning but there will be no chance for Tuesday.
"It's a blow when you lose players but that's what you’ve got the squad for at the end of the day, during the season players get injured and you have a squad that you can move around and put players in.
"We're fine, we've got enough numbers."