Lescott's injury, sustained in the 3-3 draw at Bolton Wanderers on Saturday, is a further blow for manager Mark Hughes whose side lost 3-0 at Tottenham Hotspur on Wednesday to leave them with just one win their last 10 Premier League games.
England international Lescott suffered the injury when he kicked thin air at Bolton, City's website said.
"His full-blooded airshot resulted in him hyper-extending his knee. His knee locked due to a floating piece of bone that came loose in the joint," the club said.
"Joleon had a 10-minute operation to remove the rogue chip of bone and will start his recovery programme in a couple of weeks after a precautionary delay for natural wear and tear."
Wednesday's defeat at Tottenham was a worrying performance for Hughes who spent more than 100 million pounds on transfers in the summer, including the 22 million splashed out on Lescott.
They were toothless in attack and too-easily undone at the back where 35-year-old full back Silvinho was given a torrid evening by England winger Aaron Lennon.
With Lescott out injured, along with left back Wayne Bridge, Hughes may well be busy again in the January transfer window with defenders his main target especially as Lescott's central defensive partner Kolo Toure is off to the African Nations Cup.
"Lescott's had the operation and he's going to be missing, so that compromises us somewhat, with Kolo due to go away as well," Hughes said. "We'll have to look at what we've got at the back in terms of cover.
"At the moment we are having problems dealing with balls that come into our box."
City were widely tipped to threaten the established top-four in England this season but are now down in eighth place, their lowest position of the season.
