The Serie A club named Stephan El Shaarawy among their A List players, overlooking the fact that he is eligible for the B List.
That list is designed for players born after January 1, 1992, who have served at least two years at the club.
As a result, Niang was not included in the 25-man squad named on Tuesday.
Club director Umberto Gandini took the blame for the error.
A statement on the club's official website read: "Umberto Gandini, director of AC Milan organisation, has assumed the responsibility for the error in the completion of the lists (for the) Champions League.
"Gandini regrets this error and apologises to all parties concerned and professionally to the Rossoneri fans."
Milan were handed a tough draw in the Champions League group stages, with Barcelona, Ajax and Celtic joining them in Group H.
