Celtic, who were knocked out of the UEFA Champions League following the 3-0 loss to the Serie A side, insisted the banners, which appear to pay tribute to an IRA terrorist, were not approved by the club.
But European football's governing body confirmed on Wednesday that disciplinary action would be taken.
"Disciplinary proceedings have been opened against Celtic FC for an incident of a non-sporting nature (illicit banner: Art. 16.2 of the disciplinary regulations) at (Tuesday) night's UEFA Champions League match against AC Milan in Glasgow," a UEFA statement read.
"The case will be dealt with by the UEFA Control and Disciplinary Body meeting on December 11."
Celtic chief executive Peter Lawwell told the club's official website: "Last night was nothing more than clear disrespect for the club and our supporters, who now face another UEFA charge.
"There have now been a number of UEFA charges made against the club during the last three years, relating to behaviour, displays and pyrotechnics - it cannot go on any further.
"Let's be very clear. Following the actions of a small minority, these charges are made against the club. It is the reputation of Celtic, our great club and our great fans which is damaged, while others carry on indulging in such behaviour."
In 2012, Celtic were fined £21,000 by UEFA after being charged with "the displaying of a banner of an offensive nature and the setting off of fireworks by supporters" at a Europa League game in Italy against Udinese.
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