No one was injured in the blaze, though it did damage the attic, roof and one of the building's cupolas.
Battalion Chief Mike Giannini described the damage as minimum to moderate, saying that sprinklers helped firefighters douse the flames.
"Star Wars" fans worried about any harm to potentially valuable collectibles can relax -- the fire only damaged office supplies and furniture.
Giannini also said that Skywalker Ranch, the 4,000-acre estate the iconic director uses as a "retreat," has its own fire brigade. It was those firefighters that first responded to the blaze.
Authorities are still investigating the source of the fire, though it could have started with the electric motor of an exhaust fan.