Reports indicate firefighters were called to the Fortinos at 1059 Plains Road East around noon today (Oct. 2).
Those who were in the store at the time say smoke could be seen quickly spreading.
An evacuation took place and no injuries have been reported.
As of 2 p.m., the Burlington Fire Department were still at the scene dealing with fire.
According to information provided to Halton police, the fire may have started in an oven.
Fortinos has said the store will be closed for the rest of the day as investigators look into the cause of the fire. Crews are also on hand to deal with the cleanup.
The store is expected to reopen tomorrow depending the results of safety checks.