Ulster's PRO14 game against Benetton in Treviso on Saturday has been postponed amid the spread of the coronavirus in northern Italy.
It comes as the Republic's Minister for Health Simon Harris raised doubts as to whether Ireland's clash with Italy will go ahead next month.
He said mass gatherings were something that needed to be considered with the March 7 tie at the Aviva one such event.
Thousands of Italy fans are expected in Dublin.
Government officials told the Irish Independent "too early to call" but one possibility was it would be called off.
There is precedent for Six Nations' matches being postponed during to health concerns. In 2001, two Irish games - against England and Scotland - were delayed by months in a bid to curtail the spread of foot and mouth disease.
A spokesman for the IRFU said, as things stand, all the games scheduled for the weekend of March 7 will go ahead.
However, that was subject to advice from the Government.
A spokesman for the HSE, the Republic's health service said the National Public Health Emergency Team (NPHET) would meet on Tuesday and discuss the game.
It is the worst outbreak of the virus in Europe with 165 confirmed cases in the country and five people have already died.
On Sunday morning, the Scotland versus Italy fixture in the women's Six Nations was postponed while organisers of the Venice Carnival were forced to end their event two days earlier than planned.
Benetton's Stadio Monigo is less than 20 miles from Venice in the heart of Veneto. Italy has imposed strict quarantine rules in the region, with around 50,000 people unable to enter or leave several towns for the next two weeks without special permission.
The PRO14 confirmed on Monday that Ulster's game at Benetton and Zebre's home fixture against Ospreys, both scheduled for Saturday, had been postponed with contingency planning already under way.
"Both fixtures set to take place in Italy this weekend have been postponed due to the restrictions enforced by national and local authorities dealing with the threat posed by the Conoravirus outbreak," read a statement.
Benetton have already had one cancellation this month - their game against Dragons in Newport postponed due to Storm Dennis - with the rescheduling of that fixture for next weekend at Rodney Parade ruling out one possible option to host Ulster.
The weekend of March 14, when the Six Nations will be concluding, would seem the likeliest option, with Ulster's continued involvement in the Champions Cup meaning that is the last guaranteed fallow week for the province between now and the end of the season.
Meanwhile, The Irish Government has advised people not to travel to areas of Italy hit by the virus.
The updated advice was issued by the Department of Foreign Affairs on Monday.