A banana was thrown at Constant during Atalanta's win over the weekend.
"The President Antonio Percassi personally telephoned Milan C.E.O. Adriano Galliani to pass on the club's official apologies for what happened during the Atalanta-Milan match yesterday," a club statement read.
"The conversation was very cordial and Galliani, who accepted the apologies, underlined that what happened was an isolated incident.
"Antonio Percassi will telephone the player Constant in order to officially apologise to him as well."