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The Italian internationals featured in their side's 4-2 Supercoppa triumph against Napoli, but will not be available for selection when they take on the Rossoneri next Sunday.
"Andrea Pirlo will remain behind as he looks to shake off the effects of a heavy bruise sustained during the Super Cup victory over Napoli," a statement on the club's official website read.
"He is joined by Gigi Buffon, who will undergo a personalised training program in Vinovo."
In the 18 times the two clubs have met in the competition, both sides have won nine matches each, with Milan being the most recent victor having emerged 2-1 victors in last season's edition of the event.