Richards could not immediately undergo a scan due to swelling after being forced off in the 84th minute of a match that went on to become the longest in Premier League history due to injuries to the right-back and visiting goalkeeper Michel Vorm.
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Richards required oxygen on the pitch after appearing to twist his knee unchallenged when turning to clear a cross.
"I'm not sure what Micah has done yet - we think he has a problem with his knee but we won't know until next week," Mancini told the club's official website on Saturday. "I obviously hope he will be OK."
The City academy graduate's start to the season was interrupted by a foot injury but he had made four consecutive appearances in October.