A banner in the Celtic section of the crowd at their game against Shakhtar Donetsk in Warsaw read 'F*** the Crown' while another said 'Sorry for your loss Michael Fagan', a reference to the intruder who broke into the Queen's Buckingham Palace bedroom in 1982.
A UEFA statement read: "Please be informed that proceedings have been opened against Celtic FC regarding a banner displayed during their UEFA Champions League match against FC Shakhtar Donetsk played on September 14 in Warsaw.
"The UEFA disciplinary bodies will decide on the matter in due course."
Rangers though will face no disciplinary action over the singing of God Save The King before their match against Napoli on Wednesday evening.
European football's governing body had issued instructions for the anthem not to be sung before matches in its competitions this week, following the death of the Queen seven days ago.
However, a passionate rendition of the anthem followed a minute's silence at Ibrox that had been permitted by UEFA.
Despite the instructions not to sing the anthem, UEFA confirmed on Thursday afternoon that no action would be taken against the Glasgow club.
"This incident is not the subject of any UEFA disciplinary proceedings," a spokesperson said.
A vast silhouette of the Queen amid the colours of the Union Jack could be seen behind one of the goals before the game kicked off.
Football at all levels was postponed last weekend as a mark of respect but resumed from Monday. However, three Premier League matches scheduled for this weekend have also been postponed due to police resourcing issues linked to the Queen's state funeral, which will take place next Monday.
The league confirmed minute's silences will be observed and the national anthem will be played at the matches which are still going ahead, with players and other officials wearing black armbands.
Big screens and perimeter boards will display tribute images to the Queen and flags at grounds will fly at half-mast.
Fans will also be invited to join in a minute's applause at the 70-minute mark, to honour the Queen's 70-year reign.
Tottenham confirmed ahead of Saturday's match with Leicester that Ledley King and Emile Heskey, ambassadors for the respective clubs, will lay a floral wreath before kick-off while fans are invited to join in the pre-match singing of God Save The King, led by local artist Lanya Matthews.
England boss Gareth Southgate did not hold a press conference on Thursday to name his squad for the Nations League qualifiers.
"We recognise the country is still in a period of mourning and my thoughts remain with the Royal Family," he said.
"While it is important to explain some of our decisions around selection, we didn't feel it appropriate to hold a full press conference, when it might divert attention from where people's minds should be at this time."