The Greek government has confirmed that banks will be closed all week, after a decision by the European Central Bank not to extend emergency funding, the BBC reports.
In a decree, it cited the “extremely urgent” need to protect the financial system due to the lack of liquidity.
Cash withdrawals will be limited to €60 a day for this period, the decree says.
Athens is due to make a €1.6bn payment to the IMF on Tuesday – the same day that its current bailout expires.
In reaction to the crisis, the London, Paris and Frankfurt stock markets fell sharply in early trading on Monday, following similar falls in Asia.
The euro lost 2% of its value against the the US dollar. Government borrowing costs in Italy and Spain, two of the eurozone’s weaker economies, have also risen.
Talks between Greece and the eurozone countries over bailout terms ended without an agreement on Saturday, and Prime Minister Alexis Tsipras then called a surprise referendum on the issue to be held on 5 July.
Greece risks default and moving closer to a possible exit from the 19-member eurozone.