The teenager likely caught the virus from a bird or animal and was receiving care at a children's hospital, the province said in a statement.
The province said it was investigating the source of exposure and identifying the teenager's contacts.
The risk to the public remained low, Canada's Health Minister Mark Holland said in a post on X.
1/ The Office of the Provincial Health Officer in British Columbia has reported a presumed human case of H5 avian influenza acquired in Canada.— Mark Holland (@markhollandlib) https://t.co/tinqvb5DB5November 10, 2024
"This is a rare event," British Columbia Health Officer Bonnie Henry said in a statement.
"We are conducting a thorough investigation to fully understand the source of exposure here in BC."
H5 bird flu is widespread in wild birds worldwide and is causing outbreaks in poultry and US dairy cows, with several recent human cases in US dairy and poultry workers.
There has been no evidence of person-to-person spread so far but if that was to happen, a pandemic could unfold, scientists have said.
Earlier in November, the US disease control centre asked for farm workers exposed to animals with bird flu to be tested for the virus even if they did not have symptoms.
Bird flu has infected almost 450 dairy farms in 15 US states since March, and the disease control centre has identified 46 human cases of bird flu since April.
In Canada, British Columbia has identified at least 22 infected poultry farms since October and numerous wild birds tested positive, according to the province.
Canada has had no cases reported in dairy cattle and no evidence of bird flu in milk samples.