It is thought a flame lit bottle was thrown through the windows of the building, which is located on Smithyends above a hairdressers, on Saturday, March 16, at around 5.15am.
Police are treating the incident as wilful fire raising.
No one was hurt in the incident but the alarm was raised by a woman who lives nearby.
She heard a loud bang, and looked outside and saw flames on the wall of the building.
She contacted Strathclyde Fire and Rescue, and two appliances from Cumbernauld Fire Station attended.
Witnesses are urged to contact Cumbernauld Police Office on 01236 503900.