The 24-year-old had an operation on Monday night after sustaining the problem in City's 1-0 Barclays Premier League win over Swansea.
"The positive thing is that the injury has been repaired so the knee will be as good as new," Richards told the club's website. "I have a brace on it and I am using crutches. I can't do anything at all for the next four to six weeks and I am probably looking at 12-16 weeks before I am back in action."
The injury has also left Roberto Mancini sweating over his selection problems at right-back.
Both Pablo Zabaleta and Maicon missed the Swansea game with hamstring and foot problems respectively.
City are hopeful that both players are close to a return, with Zabaleta optimistic of being available for the weekend trip to West Ham. But should there be any setback, Mancini would be left with a major headache.
The injury comes as a personal blow for Richards in what has been a frustrating season so far. He missed the start of the campaign with an ankle injury suffered while playing for Team GB at the Olympics, and has played in just four of City's 13 games.
He was injured in the 85th minute of Saturday's game, twisting awkwardly and crumpling in obvious pain before being taken off on a stretcher.
"I knew straight away in the game that it was quite a bad injury," Richards said. "The knee locked and I couldn't straighten it.
"I suppose it could have been even worse and not repairable which would have meant removing the meniscus; so I am being positive. Injuries are all part and parcel of the job but this coming on top of the other one I do feel a little hard done to."
Source: PA
Source: PA