Two bananas were thrown at Constant and near Nigel de Jong near the end of Milan's 2-1 defeat at Atalanta.
The insult came two weeks after a banana was thrown at Barcelona's Brazilian defender Dani Alves.
Sunday's flashpoint during a second half stoppage with play deep in Atalanta's half.
Constant picked up a banana thrown at him to give to the referee, and as he did so another landed near Dutch teammate De Jong, who is of Surinamese-Indonesian descent.
De Jong and Milan's French defender Phillipe Mexes sarcastically applauded the home fans.
Milan coach Clarence Seedorf called for the banana-throwers to banned for life and applauded his players' reaction.
"It's an unfortunate incident that, thanks to the lads' professionalism, did not affect them for the rest of the game," Seedorf told Sky Sport.
"I hope that whoever was responsible will be banned from attending matches for life."
Atalanta coach Stefano Colantuono added: "The only thing I can say, since we're on the theme of fruit – whoever threw the banana should be hit on the head with a coconut.
He added: "It's the same old story, these kind of gestures are unacceptable and I'm sorry something like this has ruined a good match between the sides, and a day of celebration for us."
European football's governing body UEFA this week blasted racist attacks in Spain and called for action after fans subjected foreign players to monkey taunts and banana-throwing.
On April 27, Alves calmly picked up the banana hurled at him by a Villarreal fan and bit a chunk out of it. But there was many protests by black players after the game.