The union also said two deep cleanings of the area where the person was working were carried out over the weekend.
CBC News has contacted Maple Leaf Foods for information, but has yet to receive a response.
The union did not say what the member did at the factory.
Several meat processing plants in Alberta struggled with COVID-19 outbreaks in the spring.
The JBS factory in Brooks, Harmony Beef in Balzac, and Cargill in High River have all recorded positive cases. More than 1,500 cases of COVID-19 were linked to the Cargill plant, Alberta health officials said, with more than 940 employees testing positive.
A class action lawsuit has been filed against the company.
A security guard at the Maple Leaf factory in Brandon had previously tested positive for COVID-19 in May.
At the time, the union said the guard hadn’t been at the factory for more than two weeks and believed he fell ill after his last shift.