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.
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 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.