A fan from Kilmarnock who saw the attack, known as Dennis, said: "We were just in the pub maybe the back of 11 last night and then maybe 15 or 20 Lazio fans, well I'm assuming Lazio fans, turned up with their masks on".
The incident happened outside the Flann O'Brien pub in the Italian capital on Wednesday night.
The trajectories of both Celtic and Rangers have arced like Bonfire Night rockets through their domestic campaigns - they are level on points at the top of the Scottish Premiership and will meet in the Betfred Scottish League Cup final next month - and Thursday's Europa League ties offer the Old Firm pair the chance to make a resounding bang.
Celtic have issued a statement saying that they are aware of the incident and will provide all the help to the injured supporters.
Eyewitnesses are reported to have said that the Celtic supporters were minding their own business up until the point they were set upon by the masked men.
The duo had travelled to Rome to watch their team's Europa League clash against Lazio on Thursday, November 7, 2019 at the Stadio Olimpico. Supporters have been advised to avoid wearing the clubs colours while strolling in Rome and have also been asked to stay in large groups whenever possible and also keep a low profile.
Both teams were charged by Union of European Football Associations (UEFA) after "illicit" chants were heard during a match between them on 24 October.
Celtic were also charged over the display of an "illicit banner" during the game, which they won 2-1.
Lazio have hit a run of excellent form since their defeat in Glasgow, trouncing Torino at home and winning away to Fiorentina and AC Milan to move up to fourth place in Serie A.
Must Celtic prevail again in the Europa League, even though, it'd be very refined for Lazio to qualify for the knockout stage.