The Serbia left-back was injured in the warm-up prior to Sunday's derby victory over Manchester United at the Etihad Stadium.
Kolarov is now set to miss Champions League fixtures against CSKA Moscow and Bayern Munich as well as Barclays Premier League games against QPR, Swansea and Southampton this month.
Pellegrini said: "Kolarov has an important muscle injury in his calf so he will be at least one month
Well, I am not a doctor, but I suppose that."
Defender Eliaquim Mangala is available for Wednesday's home clash with CSKA after missing the derby but midfielder Frank Lampard is still sidelined.
Former England international Lampard had been hopeful of returning after missing four games with a thigh problem but the weekend trip to QPR looks a more likely target.
Pellegrini, speaking at a press conference to preview the crucial CSKA game, said: "Mangala has just stiffness in his hip so he is in the squad list
Frank, I think he will be fit next week."
Lampard, 36, has been missed by City in recent weeks having made a big impact since signing on loan from sister club New York City until January.
There has been plenty of speculation over whether City could seek to extend his stay and even a report that the ex-Chelsea star has already signed a deal until the end of the season.
But Pellegrini suggested such reports are premature by reiterating the position both he and Lampard have often spoken of, that no decision has yet been made.
Pellegrini said: "Frank Lampard is injured so when he recovers we can talk about that issue.
"I talked about it two months ago
We can see what happens in December
We have until December to decide."
Source : PA
Source: PA