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. The news limits manager Roberto Mancini's defensive options at a time when Kolo Toure is on international duty at the African Nations Cup.
Platt said: "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. Zabaleta struck from close range after 85 minutes as City, who had been dominant in the early stages, finally wore their resilient hosts down.
Platt said: "The pleasing thing is we battled hard, defended well and kept another clean sheet. It is pleasing from that perspective and it is also pleasing to go through.
"We knew it was going to be difficult here. You know the ball is going to come in the box and you're going to have to compete for first balls, second balls all day. It is the way it is going to be and I thought we did it well."
Platt could not comment on the one moment of controversy in the game when Stoke's Glenn Whelan escaped punishment for a two-footed tackle on City midfielder Javi Garcia early in the second half. Garcia required treatment and later had words with referee Howard Webb.
Platt said: "I haven't seen it so I can't comment on it. Somebody said it wasn't good. But the referee was right there and had a good view of it."
Stoke manager Tony Pulis also said he did not have a clear view of the incident. Pulis had no complaints about the result and felt his team had paid for trying to take the champions on.
He said: "We played more open than we normally do at home. In a cup tie you want to catch them and have a go at them. You have got to give City a lot of credit. Their attitude and approach was first class. By playing as open as we did, against the best teams, it always gives them a chance to attack and create chances. I thought they did that well."