The game was scheduled to take place in Dublin on March 7 with thousands of Italian supporters, many from the regions most affected by the outbreak, expected to make the trip.
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."
After the first three rounds of the Six Nations, Ireland and England both have nine points, four behind leaders France.
At an earlier media briefing on Ireland's preparedness for coronavirus, Ireland's Chief Medical Officer Doctor Tony Holohan said it was too soon to discuss the risks around the Saint Patrick's Day celebrations that draw tens of thousands of visitors to Ireland every March 17.