In a statement, 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 pair 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.
Some Lazio fans were filmed making fascist salutes before the previous encounter in Glasgow last month, won 2-1 by Celtic.