City have confirmed the 19-year-old, who has formed a solid central-defensive partnership with Richard Dunne this season, will be out for "a matter of weeks".
That means he will also miss out on England's friendly against France having already been overlooked for Fabio Capello's first game in charge against Switzerland.
Richards felt discomfort after Monday's defeat by Everton and the club decided to send him to London for surgery on Wednesday.
The news is a big blow for the Blues as they seek to get their European hopes back on track with winger Martin Petrov already facing a 3-match ban after being sent off against Everton.
Vedran Corluka and Nedum Onuoha are the likely candidates to replace Richards alongside Dunne, with the other slotting in at right-back.