The center back landed awkwardly following a collision with teammate Micah Richards as City practiced set pieces during its final training session before traveling 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 center 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 Kompany was sent off in the 2-0 win over Hull City 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 its 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.