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.
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 (£42; $66) 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.
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Earlier talks between Greece and the eurozone countries over bailout terms ended without an agreement, and Prime Minister Alexis Tsipras then called for a referendum on the issue to be held on 5 July.
The parliament later ratified the plan to hold a referendum.
Greece risks default and moving closer to a possible exit from the 19-member eurozone.
The euro has fallen 2% against the dollar in Monday morning trading in Asian markets.
The decree was published in the official government gazette after the Greek cabinet took the decision at a marathon session late on Sunday.
The document said the measures – including the shutting down of the Athens stock exchange on Monday – were agreed as a result of the eurozone’s decision “to refuse the extension of the loan agreement with Greece”.
The €60 restriction on withdrawals will not apply to holders of foreign bank cards.
Mr Tsipras also said that Greek deposits were safe.