Belgium centre-back Kompany struggled with a leg niggle towards the end of City's 3-0 victory at Southampton on Sunday, and now faces scans to determine the extent of his injury.
City boss Manuel Pellegrini confirmed Kompany will be assessed ahead of his side's Barclays Premier League trip to Sunderland on Wednesday night.
Given the fact Eliaquim Mangala will be banned following his red card for two bookings at Saints, Pellegrini would be forced to rejig his defence if Kompany cannot feature on Wearside
"Kompany has a problem with his hamstring, but we'll see whether it's just a cramp or an injury," said Pellegrini.
City eased past Saints on the south coast on Sunday, making light of referee Mike Jones' controversial decision not to award a penalty when Jose Fonte upended Sergio Aguero.
Jones instead booked Aguero for diving, before City took control through goals from Yaya Toure, Frank Lampard and Gael Clichy.
Southampton's first home defeat of the season carried ominous portents for a packed December that could prove to define their season.
Ronald Koeman's men face Arsenal on Wednesday, before taking on Manchester United and Chelsea during seven games across 25 days.
City, meanwhile, closed to within six points of early Premier League pace-setters Chelsea, with manager Pellegrini hailing the attitude and application of his side.
"I think that we can complain about a lot of things from this team this year, that we are conceding too many goals and not scoring as many as last season," said Pellegrini.
"But the only thing that we cannot complain about in the squad is the spirit, the personality, the character and the ambition to continue winning."
Saints must quickly refocus for Wednesday's daunting trip to Arsenal, with manager Koeman immediately demanding more attacking impetus.
"In the second half I thought little by little we would create little chances to win the game," said Koeman.
"But it was not good enough.
"It is far harder to create chances against a team like Manchester City: that was not good enough from us, and we got punished for that.
"We just have to be better than that against the top teams."
Source: PA