Richards suffered the setback when on Olympic duty for Great Britain in the quarter-final clash with South Korea. City initially thought Richards would only be out of action for a week but the prognosis is worse than first feared.
Speaking after the 3-2 win over Chelsea at Villa Park, Mancini said: "With Micah, we thought it was a small injury but instead he will longer."
He added: "He has a problem with his ankle, a big problem maybe, and it may be one month out."
Goalkeeper Joe Hart was also ruled out with a back problem which has also means he is not available for England's friendly with Italy on Wednesday.
Mancini said: "Joe had a problem with his back but I don't think it is serious."
Chelsea boss Roberto Di Matteo claimed the red card issued by referee Kevin Friend was the key moment in the game.
He said: "It changed the game in favour of Manchester City. We competed very well and at that point were in the lead.
"It was difficult in the second half against 10 men. The challenge had no intent to hurt the opposition. It was a sliding tackle and he got the ball as well.
"Sometimes a red card is given in those circumstances, sometimes it is not. But there was no intention to harm the opponent."
Source: PA
Source: PA