The 30-year-old was making his first start since early May during Wednesday's EFL Cup victory over the same opposition, but was forced off late in the game.
City have confirmed that the injury is not a recurrence of the calf problem which has troubled him recently, but also refused to put a date on his return.
"City skipper Vincent Kompany is receiving treatment for a groin injury sustained in Wednesday's EFL Cup win over Swansea," read a statement on the club's official website.
"No date has yet been set for his return. The positive for Kompany and City is that the injury is not a recurrence of the calf problems that disrupted his progress last season."
Kompany has now suffered 30 injury problems in the last four years.