The Viola supporters threw missiles at the Rossoneri official during the Serie A match between the two teams in Florence.
"Fiorentina apologise if anyone has shown a lack of respect to Milan and Galliani, a director who enjoys our highest esteem," reads a statement from the club.
"We will evaluate the photos and images of those excited moments in the presidential box. If someone has behaved incorrectly, they will no longer set foot in there.
"Of course, Galliani has not helped to calm people down - he almost tangled with a child. But, we repeat, we apologise and we will make sure that certain things do not happen again."
The match ended in a 2-2 draw.