Police say they are evacuating buildings in the area and asking the public to stay away from the crash site.
Congressman Lou Correa, who represents the district in Orange County, about 25 miles (40 km) south of Los Angeles, said the damaged building was a furniture factory.
In a message on X, Correa said at least a dozen of the victims were factory workers.
Aerial photos of the scene show parts of the plane inside the building. The accident also caused a fire, which was extinguished by firefighters.
According to local news agencies, videos taken from the building opposite show a loud explosion.
“People are just shocked by the situation,” said witness Mark Anderson KRTC-TV, external.
“It was just a big bang and then one of the people came out and said, ‘Oh my God, the building is on fire.’
The area where the plane crashed is near the Fullerton Municipal Airport, about 6 miles (10 kilometers) from Disneyland.
According to KRCA-TV, the plane was returning to the airport shortly after takeoff.
It is the second plane to crash in the area in the past two months, according to CBS, the BBC’s American partner.
On November 25, another plane crashed into a tree about one block from the site of the latest crash. Without the main ones No injuries were reported in this accident.
