Mr Snowden leaked files to the Guardian and the Washington Post showing the extent of US electronic spying.
He has said he acted to "protect basic liberties for people around the world".
But the Conservative MP said the move had been "criminally irresponsible" and "extraordinarily damaging".
At an event in Washington hosted by the American Enterprise Institute, a conservative think tank, Mr Fox said terrorist groups had been learning from the leaked data how best to avoid being monitored by the US intelligence agencies.
'Treason'Revealing the "mechanics by which the intelligences services go about their business" had been "extraordinarily damaging", he argued, but "to go into details of the names of agents and operatives is criminally irresponsible".
Mr Snowden has been granted temporary asylum in RussiaIt had shown a "total disregard for the people who are involved on the sharp end, the decent patriotic people who put their lives on the line for our countries", he continued.
In an article for the Wall Street Journal, published on Monday, he accused Mr Snowden of "treason".
Mr Fox wrote: "Not only did Mr Snowden show how the NSA intercepts emails, phone calls and radio transmissions of the Taliban in Pakistan; he also revealed email intercepts regarding Iran and the global tracking of mobile phone calls looking for unknown associates of non-intelligence targets.
"Mr Snowden also told the South China Morning Post about how the NSA hacks into computers and mobile phones in China and Hong Kong."
Mr Fox argued that it remained to be seen "just how much damage has been done to the West's security architecture as a result of the Snowden disclosures".
The MP criticised Mr Snowden for not having exhausted "all legal and constitutional options to express his reservations about the intelligence and security services".
The coverage of the files, which was recently awarded the Pulitzer Prize for public service journalism, had not contained any evidence of illegal or unreasonable activity by intelligence agencies, he contended.
Code breach"He did not attempt to limit any potential damage in making his point," Mr Fox concluded.
"Let us be clear about the intent and impact of his actions. Let us be clear to the American people and their allies about the threats they now face from enemies inside and out, terrorist and criminal.
"For once, let's say what we mean. Let us call treason by its name."
In 2013, Mr Snowden told the Guardian: "The NSA has built an infrastructure that allows it to intercept almost everything. With this capability, the vast majority of human communications are automatically ingested without targeting.
"If I wanted to see your emails or your wife's phone, all I have to do is use intercepts. I can get your emails, passwords, phone records, credit cards.
"I don't want to live in a society that does these sort of things. I do not want to live in a world where everything I do and say is recorded. That is not something I am willing to support or live under."
Mr Snowden also said he did not believe he had committed a crime: "We have seen enough criminality on the part of government. It is hypocritical to make this allegation against me."
Mr Rusbridger said the paper had "made very selective judgements"' about what to publishGuardian editor Alan Rusbridger has said that senior officials in Whitehall, the US administration and the US senate's intelligence committee had told the paper "no damage" had been caused by the leaks.
He said the paper had "made very selective judgements"' about what to publish from the files and had not revealed the names of any officials.
The coverage had prompted much-needed debate about the scale of intelligence activities and exposed the limits of laws drawn up in the pre-internet era, Mr Rusbridger argued.
Mr Fox resigned from his cabinet position in October 2011 over his relationship with Adam Werritty, who described himself as an adviser to Mr Fox on business cards, despite having no official role in government.
Mr Werritty visited Mr Fox in the Ministry of Defence on a number of occasions, and was allowed to accompany him on foreign trips where he met diplomats, defence staff and defence contractors.
An investigation by then Cabinet Secretary Sir Gus O'Donnell found Mr Fox had "clearly" breached the Ministerial Code, but he was cleared of making any financial gain through the relationship or breaching national security.