Richards suffered the injury in City's 1-0 win over Swansea as he attempted to clear a cross. He spent several minutes down on the pitch before being stretched off by medics. The operations was conducted late Monday and Richards is already on crutches.
In an interview with the club's official website, the defender had this to say about his injury.
"The positive thing is that the injury has been repaired so the knee will be as good as new. 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. I knew straight away in the game that it was quite a bad injury. The knee locked and I couldn't straighten it."
While the club has not put any official time line on Richards return, a four-month layoff is expected.