Lavabit LLC, a highly encrypted email service created in 2004 by Texas programmers who had concerns about Gmail privacy protections, did not spell out the reason for the shutdown, which affects some 350,000 customers.
But Kurt Opsahl, senior staff attorney for the non-profit digital rights Electronic Frontier Foundation, told British newspaper The Guardian he believed the government had a court order for Lavabit's data.
The Washington Post said Snowden's own account might be at issue.
Wired technology news website said the circumstances must have been extraordinary because court records indicate Lavabit complied with a routine search warrant in June. That warrant targeted a child pornography suspect in a federal case in Maryland.
Opsahl told The Guardian Lavabit appeared to be the first technology company to shut down rather than comply with a court-sanctioned government surveillance order.
"I am unaware of any situation in which a service provider chose to shut down rather than comply with a court order they felt violated the Constitution," he said.
He added he considered the decision by Lavabit owner-operator Ladar Levison "a very bold stand."
"I have been forced to make a difficult decision: to become complicit in crimes against the American people or walk away from nearly 10 years of hard work by shutting down Lavabit," Levison wrote on a splash screen that replaced the normal Lavabit homepage.
"After significant soul searching, I have decided to suspend operations," Levison continued.
"I wish that I could legally share with you the events that led to my decision. I cannot," he said in his post, which also appeared on the Lavabit Facebook page. "I feel you deserve to know what's going on -- the First Amendment is supposed to guarantee me the freedom to speak out in situations like this.
"Unfortunately, Congress has passed laws that say otherwise. As things currently stand, I cannot share my experiences over the last six weeks, even though I have twice made the appropriate requests," he said.
Levison said Lavabit was now preparing to make an appeal to the 4th U.S. Circuit Court of Appeals in Richmond, Va., which has appellate jurisdiction over U.S. District Courts in parts of five states, including Virginia and Maryland, where many U.S. intelligence agencies are based.
The National Security Agency, whose documents Snowden started leaking in June, is based in Fort Meade, Md.
A favorable decision by the circuit court "would allow me [to] resurrect Lavabit as an American company," Levison wrote.
"This experience has taught me one very important lesson: without congressional action or a strong judicial precedent, I would strongly recommend against anyone trusting their private data to a company with physical ties to the United States," he concluded.
The NSA, Justice Department, White House and the Office of National Intelligence Director James R. Clapper had no immediate comment.