Leo Varadkar confirmed the November visit was cancelled and said the "US side has cited scheduling reasons".
Last month the USA president announced his intention to come to Ireland taking the government by surprise.
The White House announced in August that Mr. Trump would be visiting Ireland.
The Irish cancellation came on the same day that the Kremlin organ Tass reported Trump could be meeting with Russian President Vladimir Putin at some point during that Paris trip.
Mr Coveney said: "It will be controversial because everything Donald Trump does these days is controversial".
Brendan Howlin, the leader of the Labour Party in the Republic of Ireland, said that Mr Trump was "no friend of democracy or human rights".
Mr Trump was apparently planning to spend a day in Dublin before travelling to Doonbeg, Co Clare, where he owns golf links.
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The White House had said the Irish visit would "renew the deep and historic ties between our two nations".
Preparations for street protests over the visit were already under way when it emerged Mr Trump has cancelled his trip.
Mr Varadkar admitted at the time the president's decision to come to Ireland "came a little bit out of the blue".
Trump's family business operates a golf club on Ireland's west coast.
Two Independent Alliance Government ministers - Finian McGrath and John Halligan - had planned to take part in the protests.
The trip to Ireland would be Trump's first to the country as President but his reception there was expected to be frosty. "I think we have to treat his office with the respect it deserves".