The US Homeland Security and Governmental Affairs Committee contacted Amazon "for an explanation" after it learned that Amazon was hosting the site, Lieberman said.
"This morning Amazon informed my staff that it has ceased to host the Wikileaks website. I wish that Amazon had taken this action earlier based on Wikileaks' previous publication of classified material," Lieberman said.
"Wikileaks' illegal, outrageous, and reckless acts have compromised our national security and put lives at risk around the world."
He said that no "responsible company" should host the material. He also said that he intends to ask Amazon about the extent of its relationship with Wikileaks and about what it will do in the future to make sure that its services are not used to distribute stolen or classified information.
Since Amazon prides itself on the ease of using its cloud services, that could be tricky. Anyone with a credit card and an internet connection can sign up for and start using Amazon Web Services.
Amazon did not reply to a request for comment.
The State Department cables are the second major release of classified US government documents published by Wikileaks.
The first, issued earlier this year, included hundreds of thousands of documents about the wars in Iraq and Afghanistan. US government officials have decried the release of the confidential documents that sometimes contain embarrassing details about relationships with other governments.
Wikileaks has moved its hosting back to the Bahnhof ISP in Sweden, according to DNS checks.