The 24-year-old, who has only recently returned to first-team action, collapsed to the turf under no pressure before being given oxygen on the pitch and replaced by Kolo Toure
Chasing back to cover a quick counter-attack from the away side, the England international appeared to twist his ankle while trying to position himself.
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The news will come as a blow for Mancini with fellow right-backs Pablo Zabaleta and Maicon also ruled out through injury, with Kolo Toure coming on as the 24-year-old's replacement.
City boss Roberto Mancini said he is unaware of a timescale for Richards' recovery, stating he will need to wait until the England international undertakes a scan to diagnose the extent of the damage.
"I'm not sure what Micah has done yet," he told the club's official website. "We think he has a problem with his knee but we won't know until [his scan] next week, I obviously hope he will be OK."
Richards has only recently returned to full fitness following a succession of niggling setbacks, with Saturday's game against Swansea only his third Premier League appearance of the season.
City face Ajax and Real Madrid in two crunch Champions League clashes within the next four weeks, along with the visit of Tottenham and a trip to Stamford Bridge to face Chelsea.