N’Diaye, 27, over-extended his leg during the 2-2 draw in Turkey on Thursday, and was taken off just before half-time.
A scan on Friday revealed a severe strain for the centre-back.
“He will miss Sunday’s match against Evian and we are working on the basis of a three-week absence,” OM coach Elie Baup said in a club statement.
N'Diaye has emerged as a first-team player this season following the sale of Stephane M’Bia to QPR.
He had previously spent most of his Marseille career out on loan at Ajaccio, Reims, and Creteil.