The F/A-18E Super Hornet was being flown on a routine training mission when it went down around 10am local time, Lieutenant Commander Lydia Bock, public affairs officer for the Joint Strike Fighter Wing, said.
Search and rescue teams scoured the crash site, but have so far been unable to locate the pilot, Lt Cmdr Bock added.
The seven injured people were at a scenic overlook where aviation enthusiasts watch military pilots flying low through a steep and narrow chasm dubbed Star Wars Canyon.
Injured tourists told KABC-TV they were taking photos of the sweeping landscape when the jet screamed into view and suddenly slammed into the canyon wall.
The news station said they were treated for minor burns and cuts from flying fragments after the plane crashed and exploded.
US and foreign militaries train pilots and test jets in the gorge, officially called Rainbow Canyon, near the park’s western entrance. Military flights there date back to the Second World War.
The chasm was nicknamed Star Wars Canyon because the mineral-rich soil and red, grey and pink walls resemble the home planet of Star Wars hero Luke Skywalker.
Lt Cmdr Bock said the cause of the crash was under investigation.
The jet was from strike fighter squadron VFA-151 stationed at Lemoore. The squadron is part of an air group attached to the aircraft carrier USS John C Stennis.
Additional reporting by agencies