The centre-back landed awkwardly following a collision with team-mate Micah Richards as City practiced set-pieces during their final training session before travelling to Liverpool for the crunch meeting at Anfield.
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Should Kompany fail to shake off the injury, Manuel Pellegrini will be forced to shuffle his pack and could potentially start with holding midfielder Javi Garcia at centre-back.
The Spaniard has had experience playing at the back for City, with the 27-year-old former Benfica star occupying a central defensive role when, ironically, Kompany was sent off in the 2-0 win over Hull City back in March.
Joleon Lescott could also get the nod to start alongside Martin Demichelis, with Matija Nastasic still recovering from a knee injury and having not featured for the club since February.
The absence of the influential Belgian would come as a massive blow to City and their title bid, with Pellegrini facing up to the prospect of taking on deadly strike duo Luis Suarez and Daniel Sturridge without his key central defender.