The decision of the European Central Bank means Greek lenders will have no way to replenish fast diminishing deposits.
Tsipras says capital controls will be introduced on the recommendation of the Bank of Greece.
"This decision, today, led the European Central Bank to not increase the liquidity to Greek banks and forced the Bank of Greece to recommend measures for a bank holiday and a limit on bank withdrawals. It is more than clear that this decision had no other goal but to blackmail the will of the Greek people and obstruct the smooth democratic process of the referendum. But they will not succeed."
While Tsipras sought to reassure people that their deposits are safe, he gave no details of how long banks will remain closed or what restrictions will be placed on transactions.
The developments have thrown into question Greece's financial future and continued membership in the Eurozone and even the European Union.
Over the weekend, Greeks have been rushing to ATMs to withdraw money following Tsipras' sudden decision to call a referendum on creditor proposals for Greek reforms in return for vital bailout funds.
Since Friday night alone, 1.3 billion euros have been withdrawn from the Greek banking system, according to the bank workers' union.
The government is urging Greeks to vote against the creditor proposals, arguing that they are humiliating and that they would prolong the country's financial woes.
On the streets of Athens, protesters gathered outside the European Union offices.
"We are here today to protest against the measures that the European Union wants to bring against the new austerity measures and to rally in support of the 'no' as an answer to the referendum that the government has brought and to support the exit from the European Union and the eurozone."
"As you can see here we are sending a specific message which says 'No to the agreement, overthrow the European Union and the International Monetary Fund."
However, two opinion polls published Sunday have indicated that more Greeks want to stay in the eurozone and make a deal with creditors than want to break from the country's European partners.
The country's negotiations with its European creditors have been suspended, with both sides accusing each other of being responsible.
Greece is due to make a 1.6-billion-euro payment to the International Monetary Fund on Tuesday, the same day that its current bailout expires.
The country risks default and moving closer to a possible exit from the eurozone.
For CRI, I'm Qi Zhi.
