Crews arrived on the scene after nightfall at 37 Shiff Crescent near Heart Lake Road and Bovaird Drive.
No injuries have been reported.
Emergency teams say streets are blocked in the neighbourhood, and they are asking motorists and onlookers to avoid the area.
Firefighters are trying to contain the fire to prevent it from spreading to other units in the complex, which are connected to each other.
Video footage shows water hoses directed to the ground floor of the home, possibly aiming at the garage area.
Extensive smoke can be seen in the area.