Varoufakis, a joint Greek-Australian citizen who taught at Sydney University for more than a decade, said he was standing aside at the request of Prime Minister Alex Tsipras.
It came after more than 60 per cent of Greeks voted to reject the terms of a eurozone bailout which would have imposed more austerity measures on an already ravaged economy.
In a statement on his blog, Varoufakis said he had been “made aware” that some members of the eurozone considered him unwelcome at meetings of finance ministers, “an idea the prime minister judged to be potentially helpful to him in reaching an agreement”.
“For this reason I am leaving the ministry of finance today,” he said.
In its first comments since the weekend vote, the European Commission said the stability of the eurozone was “not in question”.
Its vice president Valdis Dombrovskis told a news conference there was no easy way out of the crisis and the referendum result widened the gap between Greece and other eurozone countries.
“We have everything we need to manage the situation,” he said.
On Monday, a defiant Germany said there was “no basis” for fresh talks with Greece on a new bailout package or debt relief for the referendum.
However, the United Kingdom urged cooperation.
“Clearly Greece and the eurozone need to sit down and talk through the implications of the result and what happens next. They need to find a sustainable solution,” a spokesperson for British prime minister David Cameron said.
German chancellor Angela Merkel was due to meet French leader Francois Hollande in Paris on Monday night amid a flurry of other meetings to size up the implications of the vote.
A statement was expected from German and French finance ministers who were also expected to meet on Monday.
European Union president Donald Tusk said an emergency eurozone summit would be held on Tuesday.
Varoufakis infuriated Greece’s European partners last week when he accused creditors of using “terrorism” against the Greek people to intimidate them into accepting more austerity.