As part of the country's capital controls, no checks can be cashed, although they can be deposited. Anyone leaving the country, whether Cypriot or a visitor, can only take up to 1,000 euros ($1,290) with them in cash.
The country's general accounting office said pensions and other social security payments, together with salaries for government employees, will be in bank accounts next Tuesday and Wednesday.
Many Cypriots struggled Thursday to understand what exactly they could and couldn't do with their money. Television talk shows addressed viewers' queries, which ranged from how they would pay college tuition for children studying abroad to how to handle check payments.
People also wondered whether they would be able to access their salaries, many of which were due this week.
Some analysts are concerned that, if kept in place long, Cyprus's measures will go against the fundamental principle of the single currency: Free and easy movement of money around the euro's 17 members.
In a statement Thursday, The European Commission said "the free movement of capital should be reinstated as soon as possible".
Not every account in Laiki and Bank of Cyprus will be hit with big losses. Deposits held by the central government, local authorities such as municipalities, universities and development projects being co-funded by the European Union will not face a so-called haircut.
Government welfare and pension fund accounts in Laiki will be treated in the same way as those in the Bank of Cyprus, "thereby ensuring most of the deposits," said Constantinos Petrides, undersecretary to the president.
Some individuals and businesses had moved their money out of Cyprus well before the banks closed their doors last week.
According to ECB figures, deposits in Cyprus' banks slipped 2.2 percent last month, to 46.36 billion euros ($59.36 billion), the lowest figure since May 2010 and down from a peak of 50.5 billion euros ($64.67 billion) in May 2012. The figure excludes deposits from other banks and the central government.
"I anticipated, not this to happen, but I anticipated issues last year, when Greece had a question of whether it will remain in euro and the consequences of that," said Athos Angelides, who runs a business importing and distributing hair salon products. "So luckily we transferred money in the middle of last year over to the UK."
The stock market, which has been closed since March 15, stayed shut. It will remain closed on Friday and Monday, when most of Europe is closed for the Easter celebrations. Cyprus follows the Orthodox calendar and does not celebrate Easter until May this year.
Elena Becatoros in Nicosia and David McHugh in Frankfurt contributed.