The Communications Security Establishment Canada (CSEC) collected information gathered from unsuspecting passengers' wireless devices by the airport's free wi-fi system over a two-week period in 2012.
CSEC then tracked the travellers for a week or more as their wireless devices showed up in wi-fi "hot spots" in cities across Canada and even at US airports, the Canadian Broadcasting Corporation (CBC) quoted a top secret document retrieved by Snowden as saying.
The programme is now fully operational, CBC News quoted its sources as saying.
CSEC is prohibited by law from targeting Canadians or anyone in Canada without an appropriate warrant. Its primary task is to collect foreign intelligence by intercepting overseas phone and internet traffic.
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After reviewing the leaked document, Ronald Deibert, one of Canada's leading authorities on cyber-security, said the CSEC's clandestine operation was "almost certainly illegal".
"I can't see any circumstance in which this would not be unlawful, under current Canadian law, under our Charter, under CSEC's mandates," Deibert said.
The document leaked by Snowden did not specify which airport was targeted. Two airports - Vancouver and Toronto - and Boingo, an independent supplier of wi-fi services at Canadian airports, have denied any involvement in the matter.
Snowden, a former NSA contractor, fled the US in May last year after leaking thousands of documents that revealed intrusive internet and phone surveillance by the US and other intelligence services. He is currently living in Russia.