Proceedings were opened against the club on November 27 after certain sections of the crowd unfurled banners that appeared to pay tribute to an IRA terrorist.
Celtic, who lost the fixture 3-0 at Celtic Park to crash out of the competition, insisted the banners were not approved by the club.
But UEFA decided to take action, and the Glasgow giants have urged supporters to avoid a repeat of any such behaviour in future.
A statement on the club's website read: "Celtic can confirm that UEFA has today (Friday) imposed a €50,000 fine on the club following the display of illicit banners at the recent match against AC Milan.
"Clearly it is extremely disappointing that the club must pay another sizeable penalty following the actions of a small minority, particularly given the previous assurances which were made to the club and the widespread understanding of the likely outcome of such actions.
"Regrettably, due to previous charges being brought against the club, again following the actions of a small minority, the fines imposed by UEFA are increasing in scale.
"It goes without saying that such actions must stop now, before the club receives a competitive sanction or one which would affect our supporters attending European matches."
The news is a further blow for the Scottish champions, who imposed bans on 128 supporters on Monday following crowd trouble in a league fixture at Motherwell.
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.