The country has been hit with a sudden outbreak of the disease recently, with over 370 cases confirmed, several towns in Northern Italy quarantined and cancellations of sporting events.
The IRFU confirmed the news after a meeting between chief executive Phillip Browne and the country's health minister Simon Harris.
"At the outset we made it clear that the IRFU was supportive of the government's need to protect public health in relation to the Coronavirus," the governing body said in a statement.
"We were then advised, formally, that The National Public Health Emergency team has determined that the series of matches should not proceed, in the interests of Public Health.
"The IRFU is perfectly happy to comply with this instruction. We will immediately begin to work with our Six Nations partners to look to reschedule. I would hope to have an update on that in the coming days."
There have been no confirmed reports of coronavirus in Ireland.
"We will immediately begin to work with our Six Nations partners to look to reschedule. I would hope to have an update on that in the coming days," IRFU chief executive Philip Browne told reporters after a meeting with the health minister.
"At the very outset we made it clear to the minister and his advisers that we're fully supportive of whatever steps they feel are necessary to safeguard public health in the light of the coronavirus."
The corresponding Ireland versus Italy women's and under-20s Six Nations games, scheduled to be played in Ireland that weekend, were also postponed.
"The IRFU made it very clear from the outset that they shared the viewpoint that public health is obviously the most important factor for any government or public health expert to consider," health minister Simon Harris said after the meeting.
"I know this is going to be a source of great disappointment to so many rugby fans right across our own country and indeed beyond in relation to the impact on the Six Nations, but I think it's the right decision."
The game was scheduled to take place in Dublin on March 7 with thousands of Italian supporters, many from the regions most effected by the outbreak, expected to make the trip.
The postponement was fully expected after Harris had on Tuesday expressed serious concerns over the Italy team and fans travelling to the Aviva Stadium for the fixture and called on the government to make a decision on this.
Scotland Women's match in Italy on Sunday was cancelled but there are no other international cancellations at this stage, with England due to travel to play Italy in Rome on Saturday 14 March.