That would be a significant step towards Greece leaving the euro, though it would not make it inevitable, he says.
Queues continued to build outside some ATMs in Athens on Sunday, but cash was readily available at many of them.
Greece's finance ministry said the country's financial stability council would meet later on Sunday to consider the situation.
Asked if capital controls were now inevitable, Greek Finance Minister Yanis Varoufakis told the BBC: "This is a matter that we'll have to work overnight on, with the appropriate authorities both here in Greece and in Frankfurt."
The ECB's move comes at the end of a turbulent week of negotiations between Greece and its creditors.
On Saturday, eurozone finance ministers refused a Greek request to extend Greece's current bailout beyond 30 June, the same day that Greece has to make a payment of €1.6bn to the International Monetary Fund (IMF).
Without new funds, Greece risks defaulting.
Greece and its creditors had been locked in talks over fresh bailout money on Friday when the Greek government broke off discussions to call a surprise referendum for 5 July over the terms it was being offered.
It described the terms as "not viable", and asked for an extension of its current deal until after the vote was completed.
Four London primary schools have banned Muslim children from fasting during Ramadan, it has emerged. The Lion Academy Trust has come under fire from Muslim groups for implementing the ban across all its schools.