The government wants to stop the withdrawal rush
The move, announced by the Argentine central bank on Friday, is aimed at stemming a rush by savers to withdraw funds which could break overstretched commercial banks.
Huge crowds gathered outside banks as people tried to cash their salary cheques and get money from automated teller machines.
The BBC correspondent in Sao Paulo says there is a total loss of confidence in the system and the signs are that the situation will get even worse.
Argentina's banking system has lost about 10% of its total deposits since the start of the year, with many savers launching successful court challenges against government-imposed restrictions on withdrawals.
The government is now hoping to pass a bill that would convert most depositors' savings into 10-year bonds.
The savings-for-bond swap would make it harder for savers to have the government's $500-a-month limit on withdrawals legally overturned.
Earlier, the government ordered Canadian-owned Scotiabank Quilmes, the country's 11th biggest deposit holder, to close for 30 days.
Hundreds of people lined up outside Scotiabank's main Buenos Aires branch to withdraw their salaries, one of the few operations the bank was still allowed to perform.
Within a few hours, other banks closed branches across the city and put guards at the doors.
Cry for help
A telecoms worker, Maximiliano Lopez, who was waiting outside Scotiabank's headquarters said: "I have 12 pesos [$4] to last me until the end of the month.
"I probably won't eat much today because that much money doesn't stretch that far."
Foreign banks are faced with a choice of bailing out their cash-strapped Argentine units until the crisis is resolved, or exiting the country altogether.
Argentine Finance Minister Remes Lenicov is expected to ask the International Monetary Fund for extra aid to resolve the banking crisis at a meeting in Washington this weekend.
But the IMF had indicated that it would not make any extra cash available unless the Argentine Government pushes through an austerity package.
The IMF proposal would force Argentina to slash thousands of public-sector jobs, a move that would impose further economic hardship on the Argentine people.
Argentina's latest economic crisis, which began in earnest late last year after the country missed repayments on its $140bn debt, has been marked by violent street protests.
Earlier this week, the IMF said it expected the Argentine economy to contract by 10-15% this year.