The Hoops have also been sanctioned for "offensive chanting" while the Serie A side have also copped a €10,000 fine for the latter charge.
Celtic recorded a 2-1 victory over the Italians but the game was nearly overshadowed by events off the pitch, with Lazio fans marching through Glasgow giving fascist salutes and chanting a song popular with the Italian far-right en route to the game.
Inside the stadium, Celtic supporters group the Green Brigade displayed several banners including one inviting their opponents to "**** off" in Italian as well as one depicting Benito Mussolini hanging with the slogan "Follow Your Leader."
UEFA's response was to charge Celtic with displaying "illicit banners and chanting" while European football's governing body also sanctioned Lazio over offensive chanting.
The fine is the latest in a long line of punishments dished out to the Scottish champions by UEFA.
It is the 19th time that Celtic have incurred the wrath of European football's governing body since 2007, and their third charge of the 2019/20 campaign.
UEFA's control, ethics and disciplinary body fined Celtic more than £10,000 after supporters set off flares in a Europa League match with Romanian side CFR Cluj, while the Scottish Premiership side had to pay a similar fine after travelling fans were found to have used flares and thrown objects in the second leg of their Europa League play-off with AIK in Stockholm in August.
The Hoops could also face further charges, and subsequent fines, with UEFA still to scrutinise Celtic's 2-1 win over Lazio in Rome earlier this month.