Leo Varadkar has warned that if the UK fails to keep to EU standards, its access to the European market could be threatened.
The Tanaiste said that while the UK has the power to deviate from EU regulations, they have to "largely" follow European rules where it is relevant.
Mr Varadkar also said that the UK's access to the European market is "not unconditional", as laid out in the 1,246-page treaty.
He said the post-Brexit trade deal means British businesses do not have to pay tariffs or quotas.
The Tanaiste told Newstalk: "It does still give them access to the European single market, a market of 400 million people, the biggest and wealthiest market in the world.
"They don't have to pay tariffs or quotas either which is advantageous to them.
"But it's not unconditional. So what they have agreed to is what we call a level playing field.
"They have agreed to a non-regression clause in all but name, so 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.
"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."
Mr Varadkar said that the UK has the sovereignty and power to deviate from EU rules and regulations.
He added: "But if they do deviate too much then they lose access to the market and the truth is the lunar pull isn't a bad analogy.
"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.
"There's no way to take Britain out of Europe, you can take Britain out of the EU, but not Europe.
— Simon Coveney (@simoncoveney) December 26, 2020
"The reality is when you are surrounded by a massive market on all sides you are always going to have to be cognisant of the fact that that market has rules and regulations.
"There won't be tariffs or quotas but what there will be is customs procedures so there will be a lot of new bureaucracy for businesses unfortunately, filling in customs declarations and also there will be checks on ports and airports, so costs and delays unfortunately for businesses.
"But it could have been a much worse situation if we ended up with tariffs and quotas."
Mr Varadkar said that very little will change around travel rules for Irish citizens.
"They still will be able to travel freely to Britain and live, work and study there," he added.
"Other Europeans won't but that's a special arrangement that we have because of the Irish protocol and common travel area."