Kompany felt pain late in Wednesday's EFL Cup third-round win at Swansea, which had been his first appearance of the season, and left the field moments before full-time.
The club are still to learn the full extent of the problem and no date has been put on the 30-year-old's potential return.
There is some good news in that the injury is not connected to the calf complaints which blighted Kompany's 2015-16 campaign, but it is the latest in a long line of setbacks to have hampered his career.
The influential centre-back has now suffered 34 injuries since joining City in 2008.
His most recent absence came after he sustained a thigh injury in the Champions League semi-final loss to Real Madrid in May
He missed the final two games of last season and the first eight of the new campaign.
Source: PA