Lt. Gen. Michael Flynn, the retired chief of the Defense Intelligence Agency, made the call in an interview with Jake Tapper on "The Lead."
"If it were me, I would have been out the door and probably in jail," said Flynn, who decried what he said was a "lack of accountability, frankly, in a person who should have been much more responsible in her actions as the secretary of state of the United States of America."
Clinton campaign spokesman Brian Fallon later told Tapper the general's suggestion was "just silly" and pointed to similar FBI probes of former Secretary of State Colin Powell and of aides to former Secretary of State Condoleezza Rice.
"In both of those two cases, you now have the same agency looking at their emails, personal emails, and saying that there is information that in retrospect they think should be treated as classified," Fallon said. "The exact same situation playing out in the two previous secretaries before Secretary Clinton. So I think that tells you everything about the relative seriousness of this."
When pressed by CNN, Flynn said, "I don't have any personal evidence" that Clinton or one of her staffers took material off a classified server and put it on an unclassified server.
Since leaving office, Flynn has been fiercely critical
of the Obama administration's approach to the Middle East and has told Tapper that the President's advisors are more concerned with appearances than hard realities. Flynn said he has made himself available for advice to any presidential campaign that has asked, Democrat or Republican, and five campaigns have taken advantage of the offer, including Donald Trump's.
The FBI confirmed in a February 2 letter to U.S. District Court Judge Emmet Sullivan that it is officially investigating Clinton's use of a private server at her home in Chappaqua, New York, to conduct business while she was secretary of state.
Two government agencies have flagged emails on Clinton's server as containing classified information, according to a January 14 letter that Intelligence Community Inspector General I. Charles McCullough III sent lawmakers. Some emails were on "special access programs," a subset of the highest "Top Secret" level of classification that falls under even tougher control rules than other Top Secret information.
The Democratic presidential candidate has repeatedly pointed to State Department findings that at the time the emails were sent, the information wasn't classified. The State Department has said that some emails were classified retroactively.
The Clinton campaign has also pointed to a dispute between the State Department and the intelligence community over which kinds of documents should be classified. And it has charged that the investigation is politically motivated.
Fallon has said Clinton's campaign believes McCullough is working with Republican lawmakers to make sure the information becomes public to embarrass their candidate. Republicans asked the inspector general to investigate in March.
"This over-classification excuse is not an excuse," Flynn said Friday. "If it's classified, it's classified."
Flynn, who headed the Defense Intelligence Agency from July 2012 to August 2014, told Tapper that Clinton "knew better" given the roles that she has had as a senator, a secretary of state, "even back when she was married to the president of the United States, she was going to have privileged information in that regard."