Canadian Health Minister Rona Ambrose announced Wednesday the person who died was an Alberta resident who had recently traveled to Beijing.
Health officials are calling this an "isolated case"and believe the risk to the general population is low.
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%. Between 2003 and December 2013 there were 648 confirmed human cases of H5N1 infection in 15 countries, leading to 384 deaths.
The infected person showed signs of the flu on an Air Canada flight from Beijing to Vancouver on December 27th.
On January 1st the person was admitted to hospital where they died two days later. The H5N1 diagnosis was later confirmed.
Canadian officials were working with Chinese authorities on the case. Health officials are concerned about the H5N1 virus mutating and becoming easily transmissible between humans, since the consequences for public health could be very serious.