At a press conference in Brussels, Mr Barnier said the proposed backstop would only be feasible for Northern Ireland and not the whole UK.
He warned the Prime Minister: “Let me be very clear. Our backstop cannot be extended to the whole of the United Kingdom.
“It has been designed for the specific situation of Northern Ireland. The temporary backstop is not in line with what we want.”
Mrs May proposed the backstop idea yesterday to avoid a hard border being imposed between Northern Ireland and the Republic of Ireland.
Under the proposal, Northern Ireland would fall under EU customs union rules until a suitable replacement is worked out.
But the EU’s refusal to extend the Prime Minister’s plan will be a major blow to the UK’s negotiating stance.
Mr Barnier added: “The UK proposals cannot constitute a backstop since the issue of full regulatory alignment is not addressed.
“What is feasible for a territory the size of Northern Ireland is not necessarily feasible for the whole UK.”
In a further dig at Mrs May and Brexit Secretary David Davis, Mr Barnier accused the UK of playing the “blame game” over the issue.
The Frenchman, who arrived at the press conference 25 minutes late, told reporters: “We’re not going to be intimidated by this form of blame game.
“The UK is leaving the EU – we respect that and are implementing it. But the UK needs to accept the consequences.
“If we want to build a new relationship there needs to be more trust, but there also needs to be more realism about what’s possible and what’s not possible.”
Mr Barnier also mocked Mrs May’s “Brexit means Brexit” catchphrase, saying: “Backstop means backstop.”
Mr Barnier also warned Mrs May that time is running out to strike a withdrawal agreement with Brussels.
He said: “In less than 10 months, the UK will leave the EU – the time has come to take decisions and make choices.
“We need to achieve the agreement on an orderly withdrawal by the autumn.
“We continue to work hard and we continue to explain, very clearly, what our positions are on the single market and customs union.
“We are happy and ready to step up the frequency of our discussions and negotiations.”
The Frenchman refused to comment on leaked remarks by Foreign Secretary Boris Johnson that Brexit negotiations could go into “meltdown”.
Mr Barnier said: “We are drawing up our position taking full account of the British red lines, which have set out by Boris Johnson and his colleagues.
“We respect the British red lines, but it would also be good if Britain could respect its own red lines.”
Mrs May has refused to sack Mr Johnson following the leak, with Downing Street sources saying he retains the Prime Minister’s confidence.