Supporters displayed banners of Scottish historical figure William Wallace and IRA hunger striker Bobby Sands along with a set of lyrics as their side lost 3-0 to the Italians at Parkhead to end their hopes of European football after Christmas.
A UEFA statement read: "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.
"The case will be dealt with by the UEFA Control and Disciplinary Body meeting on December 11."
The banners, which were displayed in and around the section housed by the Green Brigade group of supporters, read: "The terrorist or the dreamer, the savage or the brave, depends whose vote you're trying to catch or whose face you're trying to save."
The rule UEFA referred to states that clubs are liable for "inappropriate behaviour on the part of their supporters... even if they can prove the absence of any negligence in relation to the organisation of the match".
The "inappropriate behaviour" includes the "use of gestures, words, objects or any other means to transmit any message that is not fit for a sports event, particularly messages that are of a political, ideological, religious, offensive or provocative nature".
Celtic were fined approximately £4,200 after supporters let off fireworks in their Celtic Park qualifier against Cliftonville in July.
Meanwhile, a 25-year-old man has been reported to the procurator fiscal after a laser pen was allegedly pointed at AC Milan goalkeeper Christian ¬Abbiati during last night's Champions League match at Celtic Park.
The goalkeeper ¬appeared to be targeted as his side beat Celtic 3-0 to end the Glasgow club's -European campaign.
A Police Scotland spokeswoman said: "We can confirm a 25-year-old man is the subject of a report to the procurator fiscal in connection with allegedly shining a laser pen on to the pitch at Celtic Park during the match."