The full-back aggravated the injury during a recent training session and has been replaced in the starting lineup by Argentine Pablo Zabaleta.
However, Richards should be fit to face Tottenham Hotspur at the Etihad Stadium next weekend.
"Micah Richards has a hamstring injury," Mancini told Sky Sports News.
"It is not serious but we cannot take any risks at the moment. He should be fit to play Tottenham on Sunday."
Richards has scored one goal this season.