The full-back left the game within the first five minutes after pulling up after making a run forward.
If the injury sustained is serious this will be a huge blow to Roberto Mancini as his side look to secure their Champions League place for next season.
The Italian boss is already without Kolo Toure, who is under suspension following a failed drugs test earlier in the year.
Richards has slowly progressed for City this year and has been an influential part of the defence that has kept 13 clean sheets this season in the Premier League.
The England international has also been a critical part of the FA Cup run to the semi-finals of the competition, where City will play local rivals Manchester United, and scored the only goal in the 1-0 victory over Reading at Eastlands in the quarter-finals.
This setback will be a big blow to Richards as he has just recently returned to form after sustaining an injury in February when he was lucky to escape long-term damage after colliding with Nigel De Jong in the 2-2 draw with Birmingham City.