The plane crashed less than two minutes after taking off from the Fullerton Municipal Airport in Orange County.
And a spokesperson for Fullerton police said it was not yet known if the people who were killed were in the plane or on the ground.
CCTV footage showed the plane was tilted on its side as it flew into the building, causing an explosion and black plume of smoke.
Of those that were injured, 10 were taken to hospital, while eight were treated and released at the scene.
The Federal Aviation Administration said the plane was a single-engine Van’s RV-10, a four-seat aircraft.
Another four-seat plane crashed into a tree a half-a-mile from the airport last November while making an emergency landing right after take-off.
Both people on board suffered minor injuries.
