The City defender sustained an injury during the warm up before Sunday's win at Fulham which a scan has revealed to be to his hamstring tendon.
"Joleon, I think, is out for at least four weeks with a problem with the muscle tendon," said Mancini.
"He went to see a doctor in London and he said it will be four or five weeks before he can come back.
"We are unlucky because Joleon is an important player for us."