In a statement on Thursday, Celtic said that the two supporters were “now in hospital and will receive every support from the club and the British consulate in Rome” after being attacked late on Wednesday night.
Italian media report that the fans were hurt in two separate incidents in the same central Rome neighbourhood, and that neither suffered life-threatening injuries.
Around 9,000 Celtic fans are estimated to be travelling to the Italian capital to watch the Group E leaders potentially seal their place in the Europa League knockout stages, with a tense atmosphere expected between the two sets of supporters.
In Glasgow last month, some Lazio fans were filmed making fascist salutes before the two teams' previous encounter.
The home supporters then mocked the Italian club's notorious far-right 'ultras' with a banner depicting Fascist dictator Benito Mussolini hanging by his feet after being killed in 1945 with the message “Follow your leader”.
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Visiting supporters in Rome have frequently been targeted by hardcore fans from the city's two clubs Roma and Lazio.
In 2013 two Roma fans were jailed for their part in a violent ambush on Tottenham Hotspur fans in the central Campo de Fiori district before Spurs' Europa League match with Lazio.
Around 50 far-right hooligans from both clubs orchestrated an attack that left one man stabbed and several others badly beaten.
The latest violent incident involving Lazio's fringe group of “ultra” supporters comes as other fans of the team pledged to change the negative “stereotype” they say surrounds the club at home and abroad.