ATHENS—Greece shut down its banking system, ordering lenders to stay closed for six days starting Monday, and its central bank moved to impose controls to prevent money from flooding out of the country.

The steps, a fateful climax to five years of debt crisis, put Greece closer than it ever has been to an exit from the euro and pushes the common currency itself into uncharted waters. The decision came after the European Central Bank—meeting in an emergency session Sunday—opted not to expand a lifeline of emergency funds that has been sustaining Greek banks while nervous depositors pulled their money out.

In response, European stocks slumped Monday and the euro fell. Greece’s stock market will be closed for as long as banks are not open to the public, the country’s Capital Markets Commission said.

On Athens’s rainy streets late Sunday, many ATMs had already been emptied. Prime Minister Alexis Tsipras’s announcement that he would call a referendum on the economic terms that Greece’s creditors want for fresh aid sent many Greeks scurrying to bank machines over the weekend to grab what remaining cash they could.

“How can something like this happen without prior warning?” asked Angeliki Psarianou, a 67-year-old retired public servant, who stood in the drizzle after arriving too late at one empty ATM in the Greek capital. “I want Tsipras to tell me how I am going to make it through the week with €10 in my bag with rent coming up. It has never been as bad as this.”

Withdrawals at bank machines will be limited to €60 ($66) a day for each account, the government said.

Greece is now cast into extraordinary uncertainty. It isn’t clear what will happen Monday when Greeks face an extended period without their money. Nor is it certain whether Mr. Tsipras can survive, politically, after his referendum next Sunday.

Now that banks have been closed, it also isn’t clear how they will reopen or, when they do, what will be the currency in their vaults and in their accounts: If Greece can’t persuade the ECB to restart emergency lending, the only practicable solution is for Greece to print its own currency so that banks can satisfy depositors and still function.

The threat of broader financial chaos prompted the Obama administration to weigh in publicly over the weekend. In Washington, U.S. Treasury Secretary Jacob Lew said he had urged the head of the International Monetary Fund and his German and French counterparts to continue to seek an emergency bailout deal for Greece despite the breakdown in negotiations.

In a separate call, Mr. Lew told Mr. Tsipras that it was “in the best interests of Greece, Europe and the global economy to find a sustainable solution that puts Greece on a path toward reform and recovery within the eurozone,” the Treasury Department said, adding that U.S. officials had also called on Athens to institute a bank holiday and controls on capital as needed.

In an televised address to the nation Sunday—his second in two days—Mr. Tsipras said it was the fault of the eurozone that Greece’s banks were now shut. European finance ministers had denied his proposal to postpone their talks until after the referendum, he said, setting off a chain reaction.

“It is more than obvious that this decision has no other goal but to stifle the will of the Greek people and to block the normal democratic procedure of the referendum,” he said.

Mr. Tspiras had pushed his eurozone peers hard during five months of negotiation, and his defiant call for a referendum—and his encouragement to vote it down—has left him with few allies in Europe.

In Germany, which is Greece’s biggest creditor, Sunday newspapers led with headlines such as “Game Over?” and the word “Exit” in ancient Greek. Leading politicians who had called for leniency with Athens in the past voiced fury, and many conservatives said it was high time for a Greek exit from the euro to be prepared.

Even in France, which has often called for a softer line on Greece, patience was wearing thin. The Socialist Prime Minister, Manuel Valls, said the ECB should keep Greece going until the referendum. But if Greeks voted “no,” he said, they would risk voting themselves out of the eurozone.

Behind the scenes this weekend, German Chancellor Angela Merkel quickly signaled that she wouldn’t support more time for Greece. The bailout agreement between Greece and its European creditors expires Tuesday.

The path over the next several days is likely to be perilous. Closing the banks essentially puts the financial system on ice, preventing a meltdown. But it doesn’t erode the intense pressure of depositors to run—and, indeed, usually strengthens it. So a dramatic turn of events would be needed to restore confidence. Either the ECB would have to restart emergency lending, or Greece would mostly likely have to revive its banks by printing the drachma.

In the end, it was the state of the banks that drew the crisis to a climax. The big Greek banks have scant cash on hand, no access to international private markets from which they could borrow, and no assets they could feasibly sell fast.

That has left them wholly dependent on loans from the ECB to be able to give cash to withdrawing depositors. As of Friday the ECB was extending nearly €89 billion in emergency loans to them on top of tens of billions more in regular funding. Those loans, known as Emergency Liquidity Assistance, or ELA, have been subject to regular review; each day the ECB has been deciding whether to grant the banks more.

On Sunday, the ECB said no more. The decision means there wouldn’t have been funding to cover further deposit flight over the weekend and on Monday.

“We continue to work closely with the Bank of Greece and we strongly endorse the commitment of member states in pledging to take action to address the fragilities of euro area economies,” ECB President Mario Draghi said.

Despite Sunday’s move, the central bank refrained from more dramatic steps that could have deepened the crisis or made it harder for the banks to ultimately reopen, such as demanding higher amounts of collateral for loans or cutting the amount of emergency loans outright.

For many months, Mr. Draghi has resisted any ECB moves that would have pre-empted political decisions in Athens and Europe about further rescue loans for Greece. “This is a political decision that will have to be taken by elected policy makers, not by central bankers,” he said on June 15.

The ECB in February said it would no longer accept Greek government debt as collateral for its standard bank lending operations, which forced Greek banks to tap the more expensive emergency-loan program to channel money to banks through the Greek central bank, which is a member of the ECB. Under ELA, banks have more leeway on what collateral to use, but they must pay a higher interest rate for the loans. The ECB can overrule ELA with a two-thirds majority.

The ECB had until recently repeatedly signed off on higher ELA funds at what became almost daily conference calls on the matter. However, ELA was kept unchanged from Wednesday through Friday.

Greek banks were able to borrow money on private markets and even sell shares to private investors as recently as last summer. But amid the bailout standoff over the past several months, their access to these sources of cash has been steadily cut off. In recent weeks, they have been living on a knife’s edge, with only lending from the ECB available to keep them open.

Domestic deposits—the amount Greek lenders owe to their local account holders—fell from €179 billion in September 2014 to €139 billion at the end of May. The banks’ reliance on central-bank funding rose from €42.6 billion to €116 billion over the same period, according to Bank of Greece figures.

The ECB on Sunday signaled that it would take additional steps if needed to calm financial markets from any contagion fears emanating from Greece to the rest of the eurozone.

The likeliest response, analysts said, would be for the ECB to scale up a €60-billion-a-month bond-buying program, commonly known as quantitative easing, if needed to show its resolve to prevent contagion from Greece from spreading to Spain, Italy and other vulnerable European economies.