According to CBS Los Angeles, the pilot ejected and was taken to a hospital, base commander Col. Melissa Coburn said at a press conference Thursday night.
There were five reported injuries on the ground, the US Air Force Reserve said in a statement.
Melissa Melendez, the assemblywoman for the district, tweeted that all warehouse workers have been accounted for.
The crash had ignited a fire but was quickly extinguished by the building's sprinkler system.
The Air Force said the aircraft was conducting a training mission.
MNA/PR