The employee was working on Monday in a lab with pigs that had been infected with the deadly virus when a tear was noticed in a protective suit.
Officials with Canada's public health and food inspection agencies made the announcement on Tuesday.
They said there is currently no risk to the public.
The unnamed employee is in self-imposed isolation and will be monitored for the next 21 days, which is the incubation period for the virus.  The employee was also offered an Ebola vaccine that has been used in clinical trials in Africa.
The employee was working in a high-security "level four" laboratory with six pigs that had been experimentally infected with the virus. The lab worker noticed a split in the suit seam after leaving the containment lab during decontamination.
The risk to fellow employees and the community "is expected to be low," said Dr John Copps, director of the  Winnipeg laboratory with the Canadian Food Inspection Agency.
People with the Ebola virus are not infectious until they show symptoms and the virus is spread through direct contact of bodily fluids, officials noted.
The National Centre for Foreign Animal Disease is part of a federal facility that does research on dangerous and contagious disease-causing agents.
The research being done with pigs on the Ebola virus at the facility was to help understand the immune reaction in swine.
An employee at the National Centre for Foreign Animal Disease in Winnipeg has potentially been exposed to the Ebola virus.