Dave Nelson of the Skyway Fire Department says someone set fire to the corner of the building, then fled.
Firefighters responded to the scene, in the 14600 block of 4th Avenue SW, shortly before 6:30 a.m. after receiving a report of flames coming from the building.
When they arrived, they found heavy smoke and fire billowing from one exterior side of the structure.
A second alarm was sent out and then a third because of the cold temperatures and the difficulty in fighting the blaze, which had gotten into the double-layered roof of the building.
"This is a stubborn fire," Nelson said. "Right now firefighters are having a difficult time reaching a certain crawl space that's in between two different levels of the building. And that's what's preventing us from getting this fire completely out."
The building originally was a school, but it was later converted into a community center that houses several programs. One of them is the Burien Little Theater, which is located in the most heavily damaged part of the building. It was being used by the Burien Actors Theatre for a performance of "Coney Island Christmas."
No one was injured in the blaze.