Simon Coveney told a Dublin conference it was time for British MPs to cast aside “unrealistic” options based on promises that cannot be delivered.
He said he feared in the absence of realism, hardliners would “win” to everyone’s cost, most notably Ireland.
UK MPs are expected to vote on the EU draft Withdrawal Agreement next week.
British Prime Minister Theresa May faces significant opposition in her bid to ratify the draft deal, including from many within her own Conservative Party.
Northern Ireland’s Democratic Unionist Party (DUP) has indicated it will vote against the deal unless there are changes, despite its confidence and supply agreement which helps keep the Conservative government in power.
The DUP has claimed the Irish border backstop aspect of the deal undermines the union between Northern Ireland and Great Britain.
But Mr Coveney argued the draft agreement was the best available to protect peace in Northern Ireland and the UK economy.
He added that while the EU was ready to provide additional clarifications on the Brexit deal, the text of the agreement could not be reopened.
The minister warned the British government that the time for “wishful thinking” was over.
He made his remarks in Dublin Castle where he and the German foreign minister Heiko Maas addressed Irish ambassadors.
The international conference addressed “Ireland’s role in a changing world”.
Mr Maas told delegates a hard border dividing the island of Ireland was unacceptable and said the issue was a fundamental concern and a matter of principle for the EU.
Meanwhile, the Taoiseach (Irish Prime Minister) Leo Varadkar has said the EU does “not want to trap the UK” with the draft Withdrawal Deal.
Speaking to reporters during a visit to Mali, he said the EU wanted to “get on” with future trade talks as soon as the deal was ratified by British and EU parliaments.
Critics of the deal have expressed fears that there is no process for the UK to unilaterally end the controversial backstop,
But Mr Varadkar said EU members were “happy” to provide more guarantees in writing about the deal before the Westminster vote.
“The summit conclusions at our last meeting in December provided written assurances, but what’s happening at the moment is there is close contact between the UK and EU institutions as to whether a further set of written guarantees, explanations and assurances could make a difference,” Mr Varadkar said.
“Our intent, once the Withdrawal Agreement has been ratified by Westminster and the European Parliament, is to get into talks on the future relationship on the new economic and trade treaty with Britain, on the new security partnership with Britain.
“We don’t want to trap the UK into anything – we want to get on to the talks about the future relationship right away. I think it’s those kind of assurances we are happy to give.”