The Riverside County coroner's office was at the scene and confirmed the crash was fatal, though it could not immediately confirm who or how many people died.
The FAA, however, said only the pilot was on board the plane.
There were no indications that prisoners or anyone on the ground was injured.
The Northrop N9M aircraft crashed just after noon at the California Rehabilitation Center on Fifth Street in Norco.
The aircraft was identified as a Flying Wing owned by the Planes of Fame Air Museum in nearby Chino.
The museum's website says the plane was built in 1944 and is considered a forerunner of the modern B-2 stealth bomber.
Northrop built four prototypes, but there was only one remaining, the museum said. The museum completed restoration of the aircraft in the 1990s and completed flight testing in 1996.
Its specs say it was just over 17 feet long and could hit a top speed of 220 mph.
"It was so unusual looking," said Susan Fracol, who witnessed the crash. "It was shaped like a stingray fish or it looked like a bat flying. It was just weird looking."
The crash triggered a fire and firefighters responded to extinguish the flames. Very little was left of the plane on the ground after the fire was extinguished.
Fracol recalls: "I saw a bright yellow plane. It made a left dip, a right dip, went forward and went nose first into the ground - and a huge fireball."
She says one of her family members knows the pilot. He was also the mechanic and was preparing the aircraft for a May 4 airshow, she said.
She says before the crash he sent a text message to friends that essentially said "Going flying, see you later for beers."
The Federal Aviation Administration and National Transportation Safety Board will investigate the crash.
#Norco Update: RSO can confirm that the Coroner’s Bureau is at the scene and assisting with the fatal plane crash. Unknown number of occupants on the plane. No other details available to release at this time. https://t.co/zV2QBLqx0n— Riverside County Sheriff PIO-West (@RSOPIOWest) April 22, 2019