Alan Dick, 55, principal of Canadian International Lower School of Hong Kong, was admitted to hospital on Sunday with severe pneumonia and a fever, the Centre for Health Protection said in a statement.
His condition deteriorated rapidly and he passed away that afternoon, the statement said.
Laboratory tests confirmed that he had the influenza A(H1N1) virus.
Dick, who joined the school in 1994, had been on sick leave for a week before being hospitalised.
Dave McMaster, head of Canadian International Upper and Lower School, said in a letter on the school's website that authorities had not yet established whether Dick's death was caused by swine flu or an underlying condition.
"The circumstances of Alan's death cannot be allowed to detract from our sense of loss for a well-loved member of our school community," he wrote. "Alan was held in the highest esteem by both current and former students and parents alike -- as demonstrated by the hundreds of Facebook and Twitter entries that have already been posted and by the flowers and messages of condolences that have been received."
The school, which is divided into lower and upper sections, reported an influenza outbreak earlier this month.
Six students were confirmed to have swine flu but they have all since recovered, the health authorities' statement on Monday said.
Dick's death takes the city's swine flu-related death toll to 23.
Hong Kong and Canada enjoy strong historical and economic links.
A large number of Hong Kong families emigrated to Canada or sent their children to schools there in the early 1990s because of uncertainty surrounding the city's return to Chinese rule in 1997.
Some families have since returned.
The Consulate General of Canada in Hong Kong estimated in June that as many as 220,000 Canadian citizens are residing in the city.
More than 500,000 Canadians can trace their family origins to Hong Kong and over one million Hong Kong residents have a relative in Canada.
The Canadian Chamber of Commerce in Hong Kong is the largest chamber outside Canada, with close to 1,000 members, according to the consulate.