The men had been drinking in the Flann O'Brien pub ahead of Thursday's Europa League match against Lazio.
Both fans are understood to have been stabbed in the leg but their injuries are not thought to be life-threatening.
One of them has since been released from hospital following treatment. Police said an investigation was ongoing.
Tensions were high after warnings that Lazio fans wanted revenge for a controversial banner unfurled by Celtic fans at a match in Glasgow last month.
A statement released by Celtic said: "Celtic can confirm that two fans have been injured after being stabbed last night. Both will receive every support from the club and the British consulate in Rome.
BBC Scotland's sports news correspondent Chris McLaughlin, who is in Rome for the game, said local police and Celtic officials were "well aware" of the threat of reprisals.
He said: "Lazio are a club that has right-wing leanings and their fans have a reputation for violence.
"There were reports of violence last night around 11 o'clock local time and a police source told me that two men had been taken to hospital.
"Both had been stabbed in the leg and both, I am told, were Celtic fans. Reports this morning suggested that one of the men is a German.
He added: "In terms of the Flann O'Brien pub, I'm told that around five or six masked men appeared from a side street and started to attack the Celtic fans randomly, for no apparent reason."
About 10,000 Celtic fans are expected in Rome for the match and an extra 1,000 police officers will be on the streets.
Chris McLaughlin told BBC Radio's Good Morning Scotland programme: "They are used to dealing with large European games and large domestic fixtures here in Rome.
"So they were well aware and, to be fair, well prepared for this. But there were warnings from Celtic for fans not to wear their colours when they were out and about on the streets last night.
"The police said to me, we don't have a problem with that. The Celtic fans can come here, they can party, they can drink - we are ready. Of course, when it comes to situations like this, there is only so much the police can do.
"Most fans I spoke to said they would heed the warnings, won't wear Celtic tops at night and will stay within the bars. Most said they were quite happy to be here and the locals had been very welcoming. But what happened in some of the bars last night is clearly worrying."
Travelling supporter Sam Houston, from Jordanhill in Glasgow, said about 15 hooded men threw chairs at the pub's locked windows and doors in a bid to get to fans inside.
He said: "We retreated to the back of the bar and the staff put the big metal shutters down and we just had to wait.
"It was horrible. We had heard all the stuff about the warnings that have been put in place. But we thought that if we were in this quiet pub we would be fine.
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"No-one was going to act brave and try and fight back. We were all just staying at the back of the bar and fearing for our lives.
"After about 15 minutes, the bar staff told us it was all clear. We headed out and a group of riot police who were out looking for the gangs escorted us to a taxi rank and we got away safely."
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