The 28-year-old was absent from Sunday's 1-0 derby victory over rivals Manchester United after injuring himself in the warm-up.
And manager Manuel Pellegrini confirmed on Tuesday that the Serb is set for several weeks on the sidelines, although centre-back Eliaquim Mangala returns for Wednesday's crucial UEFA Champions League clash with CSKA Moscow after a hip injury.
"Mangala is in the squad list for tomorrow," Pellegrini said. "But Kolarov has a muscle injury in his calf and he will be out for at least one month."
The Premier League champions entertain CSKA this week seeking their first win in Group E.
Another failure to pick up three points would further damage City's hopes of reaching the knockout stages, with games against Bayern Munich and Roma still to come.
But Pellegrini remains confident of progressing and believes their final pool match in Rome will prove decisive.
"I don't think that this game is sudden death, you can continue mathematically with a draw but it's a really important game," he added.
"It's impossible to be sure but I think this group will be decided in the last game against Roma in Italy.
"There have been times that a team has qualified with a low points total and then gone on to win the competition.
"With a winning mentality and an ambitious mind, you always have a chance. That's the way we must be."
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