The Belgium defender limped off after 33 minutes of City's FA Cup fourth-round win over Stoke at the Britannia Stadium and first-team coach David Platt confirmed he faced a spell out.
David Platt: "He has pulled his calf. We won't know how bad it is until the morning but there won't be any chance of Tuesday."
Remarkably it took City seven minutes to replace Kompany, who pulled up and headed straight down the tunnel, but City battled through to win 1-0 with a late Pablo Zabaleta goal.