The supersonic jet was on its way to the nearby Marine Corps Air Station Miramar but crashed around three kilometres away as it made its landing approach, authorities said.
Corporal Frances Goch, a spokeswoman for the station, told the Reuters news agency the plane was believed to have been from a training squadron.
One San Diego resident told MSNBC television channel that the crash shook his house several streets away in the neighbourhood and that officials were telling residents to move back.
"I knew definitely it was an explosion. ... It was pretty strong," he said.
Local television showed plumes of thick white smoke rising from the crash site in the suburb of the University City area.
The charred remains of a building were also clearly visible.