British Prime Minister Boris Johnson has caused outcry across the EU with plans to overrule aspects of the treaty it signed with the 27 member states last year.
The row has overshadowed protracted talks for a future trading partnership, which are deadlocked in several key areas.
Coveney told Ireland's lower house of parliament, the Dail, that Johnson's insistence in forging ahead with a controversial new bill put the whole process at risk.
"It's my view that even if we do get an agreement in terms of a future relationship that if there is still a threat by the (UK) to legislate to undermine the withdrawal agreement and break international law, I don't believe that any future relationship agreement will be ratified," he said.
"Because why would the EU ratify a new agreement with a country that is threatening to break an agreement that's not even 12 months old?"
Both London and Brussels say a deal on a free trade agreement must be struck by mid-October to allow time for it to be ratified before coming into force from January 1 next year.
Failure to do so would see trade conducted on World Trade Organization rules, with higher tariffs and quotas.
But London only recently claimed the Withdrawal Agreement it signed to allow it to leave the bloc in January this year threatened aspects of trade relating to Northern Ireland.
It had been agreed that Northern Ireland will remain uniquely subject to EU rules to maintain an open border with the Republic of Ireland -- a crucial tenet of a 1998 peace deal that ended 30 years of violence over British rule.
The British government has openly admitted its plans to override parts of the deal relating to Northern Ireland would breach international law.
Brussels has called for the proposals to be withdrawn by the end of the month or face legal action.
But Britain's Attorney General Suella Braverman told parliament on Thursday the government's move was "entirely proper".
"It's entirely constitutional and lawful in domestic law to enact legislation that may operate in breach of international law or treaty obligations," she said.