Richards was carried off on a stretcher after suffering the injury as he tried to clear a cross, medics trying to ease his pain with oxygen.
“I’m not sure what Micah has done yet,” Mancini said after Saturday’s nervy 1-0 home win. We won’t know until this week.”
There were no other players around full-back Richards when he appeared to twist his knee as he turned to try to clear a cross to the far post deep into the second half.
After lengthy treatment on the pitch, Richards was carried off on a stretcher in what was the longest match in Premier League history due to the injuries sustained to the City defender and Swansea goalkeeper Michael Vorm.
Richards, 24, started the game despite raising concerns about his manager’s tactics during the 3-1 defeat by Ajax in the Champions League on Wednesday.
City’s win over Swansea, courtesy of Carlos Tevez’s second-half goal, was their fourth in succession in the Premier League and it took them to within a point of league leaders Chelsea.
“It was important to get three points after defeat in midweek,” added Mancini.
“We did not play well in the first half because we were so tired and we were better in the second half.
“The players and the pitches are the same as in the Champions League. It happens sometimes that you don’t play well but we had chances to score another goal when we were 1-0 up against Ajax. We have to learn to take our chances.
“In the end the only important thing is the result. If you win you are the best manager, if you lose you are the worst.”
Captain Vincent Kompany felt the champions got exactly what they needed from the clash — three points.
“We won the game and we move on now. We are doing all right in the league. The most important thing here would always have been the result, certainly after Wednesday. We got the result.
“I don’t think it will be one of the games we will remember forever but it does put us in the position where it is comfortable enough for us to go into the West Ham game.’’
Meanwhile, City have appointed former Barcelona technical director Txiki Begiristain as their director of football in a management restructure.
The 48-year-old will oversee player recruitment, previously the remit of football administrator Brian Marwood.
Former Arsenal winger Marwood has moved to a new role as managing director of the club’s football academy.
Begiristain worked at Barcelona from 2008 to 2010 with new City chief executive Ferran Soriano.
MANCHESTER CITY: Hart; Richards (K Toure 81), Kompany, Kolarov (Balotell 46), Clichy; Nastasic, Nasri, Barry, Y Toure, Aguero (Lescott 90); Tevez.
SWANSEA CITY: Vorm (Tremmel 64); Chico, Williams, Rangel, Davies; Britton (Graham 72), Michu, Pablo (Dyer 77), Routledge, De Guzman, Ki Sung-Yeung.
Referee: M Atkinson.