Maldini, who will hang up his boots following the season's end, was expecting to have a warm farewell during Milan's 3-2 home defeat to AS Roma last weekend.
But section of the crowd chanted against him and unfurled banners criticizing him.
Maldini hit out at Milan for remaining silent over the matter but Galliani explained the club's stance in a letter to the legendary captain.
"Dear Paolo, I read your interview and I understand your sorrow," read the letter that was published on Milan's official website.
"I'm under escort, as you know, for the past two years due to the behavior of those persons who insulted you.
"It was me who took the decision to remain silent: not only because it was suggested to me, but especially because I believed, and still do, that silence is the most efficient weapon, so as not to give further space to behaviors like the one we saw on Sunday."
Maldini is considered a living Milan and Italy legend as he won seven league titles, one Coppa Italia and five Champions League trophies with the club since making his debut in 1984.
The 40-year-old will play his last match for Milan when the Rossoneri face Fiorentina away from home on Sunday.