The ECB, in a statement late Wednesday, said it was no longer able to assume there would be a successful conclusion to the Greek government's bailout talks with its lenders.
The Dow Jones industrial average, which had been up 100 points just before the ECB announcement, quickly turned negative after the news.
The ECB said the suspension was in line with existing Eurosystem rules, but emphasized that the news has no impact on the counterparty status of Greek financial institutions.
"This news will likely scare depositors and result in further bank runs. This all said, if Greece can come to an agreement with the troika, I'm sure the ECB will reinstate the waiver," Peter Boockvar, chief market analyst at The Lindsey Group, wrote in a note after the announcement.
This decision is expected to put more pressure on the new Greek government to come to a deal on the country's bailout program.
Global X Funds' Greek ETF fell more than 10 percent on the news.
The ECB's move is "not as big a deal as it seems," TrendMacro CIO Donald Luskin wrote in a note, especially in light of Wednesday morning's announcement that the ECB had authorized Greece's central bank to use "Emergency Liquidity Assistance" for Greek banks as needed.
"If you put both of today's policy moves together, what it means is that the Greek government—not the Eurosystem—will be on the hook for the collateral. But there will still be a funding mechanism for the banks, in case there is a serious run on them. That's the important thing," Luskin wrote.
Greece's new government has sought to overhaul the nation's bailout program with European Institutions. Greek Prime Minister Alexis Tsipras met with European Commission President Jean-Claude Juncker and the president of the European Union's parliament, Martin Schulz, in Brussels earlier on Wednesday.
Speaking at a news conference after their talks, Schulz said that Tsipras' trip around Europe showed that Greece wanted to embrace the region, rather than separate itself from it. He added that "both sides are fighting for mutual understanding" and both had to find compromises in negotiations over Greece's bailout program.
Schulz added, however, that "it is a difficult time again and we don't yet have the necessary solutions."
For his part, Tsipras said that the history of the EU was one of disagreements that ended in compromise and accords.
"We have the willingness to find a mutually acceptable agreement and compromise for our common future," he said.
—CNBC's Holly Ellyatt and Ben Berkowitz contributed to this report.