© Reuters.China has been vaccinating poultry against the H5N1 virus.
Calling the death an "isolated case", Ms Ambrose said the risk to the general population was low.
Ten people have died in Alberta this season from swine flu, or H1N1.
H5N1 infects the lower respiratory tract deep in the lung, where it can cause deadly pneumonia.
The World Health Organisation (WHO) says it is difficult to transmit the virus from person to person but when people do become infected, the mortality rate is about 60%.
In the latest incident, the infected person first showed symptoms of the flu on an Air Canada flight from Beijing to Vancouver on 27 December, officials said.
The passenger continued on to Edmonton and on 1 January was admitted to hospital where they died two days later. Canadian federal health officials said they would not identify the patient's sex, age or occupation.
Ms Ambrose said Canadian officials were working with Chinese authorities on the case. "The risk of getting H5N1 is very low. This is not the regular seasonal flu. This is an isolated case," she said.
According to the WHO, between 2003 and December 2013 there were 648 confirmed human cases of H5N1 infection in 15 countries, leading to 384 deaths.
Experts say that if the H5N1 virus were to mutate and become easily transmissible between humans, the consequences for public health could be very serious.
Yes, but you've still got to be 'afraid', 'very afraid' and you must by all means ignore the fact that people who die from this infection were pretty bloody screwed to begin with and probably had a list of medical health issues longer than, ok, more numerous than, the fingers on at least one hand, possibly into the finger of the other hand - but by all means, never mind! Just Ignore That! It's just not what they want you to hear.
Medical staff are 'supposed' to have the 'magic wand' which just cures everything, even stupidity, and yes, even mental illness.... (no not really). Not for the two latter anyway. Although sometimes, they are supposed to, just don't ask me how.
Human beings are just supposed to be unquestioning, stupid, gullible and easily directed. If your not that, then what are you?