Mr Trump was apparently planning to spend a day in Dublin before travelling to Doonbeg, Co Clare, where he owns golf links.
Leo Varadkar confirmed the November visit was cancelled and said the "US side has cited scheduling reasons".
A meeting has taken place today at Government buildings, between officials of both governments, and the visit has now been cancelled due to "scheduling reasons", according to a government spokesperson.
Earlier this month, the White House announced Trump would travel to Ireland as part of a trip including a November 11 event in Paris marking the 100th anniversary of the end of World War I. Washington had said that Trump would visit Ireland "to renew the deep and historic ties between our two nations".
"The president will travel to Paris in November as previously announced".
It was not announced if he originally planned to visit Northern Ireland on the short trip.
"Help us to do so if you abhor his policies on climate change, refugee migration, trade wars, military expansion, economic inequality and the whole gung-ho, misogynistic, racially divisive show".
President Trump has canceled a planned trip to Ireland, the Irish government said Tuesday, amid planned demonstrations to protest his climate policies, worldwide relations and treatment of immigrants, women and minorities.
This would have been the US President's first visit to Ireland since he assumed office in January 2017.
Virgin Media News political correspondent Gavan Reilly has suggested that the visit may be postponed rather than cancelled outright.
Irish activists espousing left-wing and environmentalist causes had pledged to hold protests.
Mr Varadkar has previously said that there is a standing invitation for any U.S. president to come to Ireland as many have in the past.
Opposition to the visit in Ireland was been expressed by the leader of the Labour Party in the Republic of Ireland, Brendan Howlin, saying Trump is "no friend of democracy or human rights".
Last week Ireland's deputy premier Simon Coveney said the Irish government was "a little taken by surprise" when the announcement was made.