Previously, officials said at least one person was treated for smoke inhalation.
The cause of the fire was under investigation. It wasn't immediately known where on the 840-foot (255-metre) amphibious assault vessel the blast and the fire occurred.
The flames sent up a huge plume of dark smoke visible around San Diego.
San Diego is the Bonhomme Richard's home port, and the ship was undergoing routine maintenance at the time of the fire.
About 160 sailors and officers were on board, Raney said — far fewer than the thousand typically on the ship when it's on active duty.
All crew members were accounted for, said Admiral Mike Gilday, Chief of Naval Operations.
"We are grateful for the quick and immediate response of local, base, and shipboard firefighters aboard USS Bonhomme Richard," Gilday said in a statement.
The 23-year-old ship has the capacity to deploy and land helicopters, smaller boats and amphibious vehicles.
Smoke rises from the USS Bonhomme Richard at Naval Base San Diego. Photo / AP
Because of its age, a fire could be particularly destructive, especially if it reached the engine room and other tight spaces with machinery, said Lawrence B. Brennan, a professor of admiralty and international maritime law at Fordham University in New York.
"The heat of a fire of this nature can warp the steel, and that can be a major problem for any ship," said Brennan.
"On an older ship, it's even more of a problem."
Two other docked ships, USS Fitzgerald and USS Russell, were moved to berths away from the fire, officials said.
