A spokeswoman for the province's Health Department says the victim was a middle-aged woman from the Fredericton area with an underlying health condition.
However, Tracey Burkhardt declined to release further details, citing privacy concerns.
She says the province has recorded about 300 lab-confirmed cases of influenza so far this season.
Burkhardt says the province still has an ample supply of flu vaccine.
The Public Health Agency of Canada says influenza cases in Canada continued to increase in the first week of January with the H1N1 strain showing up as the dominant strain, primarily affecting people between the ages of 20 and 64.