The back of the six-unit building on Centre Street was heavily damaged by the fire.
The fire started in a second-storey stairway at the back of the building just before 3:30 a.m., officials said. A newspaper delivery man spotted the smoke and called for help.
Forty firefighters were call in to extinguish the fire.
Granby's Fire Chief Pierre Lacombe said they were able to bring the fire under control before it spread too far into the building, and the damage was mostly limited to the outside of the building.
The cause hasn't been determined.
No one was injured.