The news is a big blow to City with nine games of the season left. England have been informed of the situation.
The injury, a partial tear of the hamstring tendon at its origin close to the pubic bone, forced Joleon to drop out of last Sunday’s game at Fulham at the last minute.
He had originally been selected at left-back to replace Wayne Bridge, out for a month after a hernia operation, and the injury will stretch Roberto Mancini’s defensive options even further.
The 27-year-old, signed from Everton last summer, had already missed 12 games after having an operation to remove a piece of floating bone in his knee in December.
After having his new injury scanned on Monday, Joleon has had an injection and undergone ultrasound treatment as he starts the recovery process, with the hope being that he can play some part in the closing stages of the season.