Greek banks will be closed and capital controls will be imposed, Prime Minister Alexis Tsipras says.
Speaking after the European Central Bank (ECB) said it was not increasing emergency funding to Greek banks, Mr Tsipras said Greek deposits were safe.
Greece is due to make a €1.6bn (£1.1bn) payment to the International Monetary Fund (IMF) on Tuesday – the same day that its current bailout expires.
Greece risks default and moving closer to a possible exit from the Eurozone.
Greeks have been queuing to withdraw money from cash machines over the weekend.
Mr Tsipras did not give details of how long banks would stay closed, or exactly what controls on capital would be imposed.
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.
“[Rejection] of the Greek government’s request for a short extension of the programme was an unprecedented act by European standards, questioning the right of a sovereign people to decide,” Mr Tsipras on Sunday said in televised address.
“This decision led the ECB today to limit the liquidity available to Greek banks and forced the Greek central bank to suggest a bank holiday and restrictions on bank withdrawals.”