The defender had to be stretchered from the field while wearing an oxygen mask in the second half of Saturday's win over Swansea City with what looked a serious problem.
Richards, who only played his first game of the season at the beginning of October after an injury, pulled up and clutched his knee in the 75th minute without any other player close to him.
The full-back then received lengthy treatment on the field before being carried off and Premier League champions Manchester City will now wait for the results of further analysis.
"I'm not sure what Micah has done yet," said manager Roberto Mancini.
"We think he has a problem with his knee but we won't know until next week. But I obviously hope he will be okay."
The injury would add to Mancini's lack of players due to fitness problems and he was already without David Silva, Pablo Zabaleta, Javi Garcia, Maicon and Jack Rodwell.
James Milner is also suspended after his red card in last weekend's win over West Bromwich Albion.