His comments were the first major reaction from Brussels since Britain announced on Monday that Prime Minister Theresa May will trigger the two-year divorce process on March 29.
"When a country leaves the union there is no punishment, there is no price to pay to leave. But we must settle the accounts, no more, no less," Barnier, a former European Commissioner and French minister, said in Brussels.
"We will not ask the British to pay a single euro for something they have not agreed to as a member," he told an EU regional institution.
Barnier said Britain had outstanding obligations for regional funding, development funds and European Commission chief Jean-Claude Juncker's investment plan, which together total obligations for the whole EU of more than 600 billion euros.
"All these programmes, we approved them together at 28, with the United Kingdom, we finance them together at 28, we benefit from them, at 28," he said.
After last year's Brexit vote EU officials said that Britain's exit bill would be around 60 billion euros, but Barnier's team is now backing away from mentioning a set sum.
Talks on a future trade deal cannot start until the terms of Britain's exit, including what it must pay, are all settled, Barnier added.
Uncertainty over the fate of 4.5 million EU citizens in Britain and vice versa must also be resolved, he said.
London has argued that the two paths can be negotiated in parallel.
"The quicker we agree on the principles of an orderly withdrawal the sooner we can prepare these future relations," Barnier said.
"Conversely, if we do not end these uncertainties and push them to the end of negotiations, we will be headed for failure."
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