LEO Varadkar has said Britain must abide by strict conditions in order to secure continued access to the European single market.
The tánaiste's remarks follow the eleventh hour agreement between Britain and the EU on a post-Brexit trade deal.
After months of negotiations, an agreement was finally struck on Christmas Eve between the two sides after they overcame the main stumbling block of fisheries.
The Stormont executive is expected to meet today to discuss the UK-EU trade deal, while the Dublin coalition cabinet will discuss the 2000-page-plus document tomorrow.
Mr Varadkar said yesterday that while Britain now had access to the European single market and could conduct tariff-free trade, the deal was "not unconditional".
He said the two sides had agreed to the so-called level playing field and a "non-regression clause in all but name".
"We said you can only have access to the market if you don't reduce your standards when it comes to workers' rights, the environment, health and safety, product standards – all of those things," he told Newstalk.
"If they do reduce their standards or don't keep with our standards then that access to our market could be threatened – they have to largely follow European rules where they are relevant."
The Fine Gael leader said Britain had the power to deviate from EU rules but any significant departure would jeopardise the deal.
He said the UK's relationship with the EU was analogous to "the lunar pull".
"You can't get away from the obvious geography that Britain is in Europe, geographically, and if Europe is the Earth then Britain, which is much smaller, is the moon," he said.
"There's no way to take Britain out of Europe, you can take Britain out of the EU, but not Europe."
He said that while there would not be tariffs or quotas, Britain would have to adhere to customs procedures and a "lot of new bureaucracy for businesses unfortunately".
Mr Varadkar said that very little will change around travel rules for Irish citizens travelling to Britain and vice versa.
He also said there will be duty free when flights recommence between Britain and Ireland.
The striking of the deal was welcomed by Taoiseach Micheál Martin, who voiced hope that it would be speedily ratified by both Westminster and Brussels ahead of coming into force on January 1.
He said the agreement represented a "good compromise and a balanced outcome" but added that there was "no such thing as a good Brexit for Ireland".
"I believe the agreement reached today is the least bad version of Brexit possible, given current circumstances," he said.
First Minister Arlene Foster said the Stormont executive was united in supporting the need for a trade deal.
"This is the start of a new era in the relationship between the UK and the EU and in Northern Ireland we will want to maximise the opportunities the new arrangements provide for our local economy," the DUP leader said.
In a personal statement sent separately, Mrs Foster said details of the trade deal, as well as other issues including security, would be examined.
Deputy First Minister Michelle O'Neill said the executive as a whole would scrutinise the deal.
"While we have distinctly different political positions on leaving the EU, we are all agreed that it's in no-one interests to leave without a deal, therefore this announcement is good news which will be welcomed across the whole island," she said.
"As an executive we will now need to consider the detail of the agreement because there will be many questions on what the agreement means for businesses and citizens and it is important they get that clarity."
SDLP leader Colum Eastwood said the deal "will not undo the enormous damage caused by Brexit to people, businesses and communities in Northern Ireland".
"This entire Brexit fantasy is a future that people here do not want and did not vote for," he said.
Alliance Party MP Stephen Farry said his party will study the deal over the coming days.
"Key considerations for us will include matters beyond just trade, such as data adequacy recognition, justice, policing and security, plus access to the full spectrum of EU programmes," he said.
But Ulster Unionist Party leader Steve Aiken said there is "no cause for celebration".
"We have achieved a 'least worst option' for UK as a whole - for Northern Ireland we now have an Irish Sea border with reams of non-tariff barriers being installed from January 1. Nothing historic about it," he said.
