Mr Trump had been expected to visit Ireland in November as part of a trip to Europe for Armistice Day celebrations.
There was confusion earlier when the White House Press Secretary Sarah Sanders told reporters that they were still finalising whether Ireland would be a stop on President Trump's upcoming visit.
"The president will travel to Paris in November as previously announced. We are still finalising whether Ireland will be a stop on that trip. As details are confirmed we will let you know," Ms Sanders said.
However, later in the evening, the White House confirmed to the Irish ambassador in the US that the trip was off "for scheduling reasons".
Mr Trump was expected to visit his golf course in Doonbeg, Co Clare, and Dublin around the weekend of 10-11 November.
An advance party from the White House was due to visit Ireland in the coming weeks to plan the trip but that has been cancelled.
The White House announced on 31 August that Mr Trump would travel to Paris to participate in a commemoration of the 100th anniversary of the Armistice that ended the fighting in World War I.
That event takes place on 11 November. Mr Trump's visit to Ireland was due to coincide with that trip.
Last month, the White House said Mr Trump would visit Ireland as part of a wider trip to Europe to "renew the deep and historic ties between our two nations".
The Government said at the time it would provide an opportunity to follow up on issues discussed by Taoiseach Leo Varadkar and Mr Trump in the White House in March, which included migration, trade, climate change and human rights issues.
Following the confirmation of Mr Trump's visit, there had been calls for protests. The Labour Party, Green Party and Solidarity-People Before Profit pledged to organise protests surrounding the visit.
Mr Varadkar said there is a standing invitation for any US president to come to Ireland and many have in the past.
Sources in the Department of An Taoiseach and the Department of Foreign Affairs have said the cancellation comes as a considerable surprise to Mr Varadkar and to the Government.