The Japan Coast Guard said the collision, which left one person injured on the destroyer, occurred about 100 km southwest of Yokosuka.
The collision was first reported by the Philippine container at around 2:30 a.m. local time (1730 GMT Friday), according to the coast guard.
The Japan Coast Guard said it believed the Philippine merchant vessel is the ACX Crystal, which, according to Japan's public broadcaster NHK, is 222.6 meters long and weighs 29,060 tons.
The USS Fitzgerald is 154 meters long and weighs 8,315 tons.
NHK reports said the US guided-missile destroyer had suffered considerable damage to its right side, with helicopter footage revealing an orange hose on the deck of the destroyer.
Crew members, according to local media images, could be see on the deck of the Aegis-equipped destroyer assessing the damage while a Japan Coast Guard vessel was in the vicinity of the ship to offer assistance.
More patrol vessels and a helicopter would be dispatched to the collision site, Japan's coastguard said.
NHK's aerial footage showed that the Philippine ship, which was sailing towards Tokyo, had scrape marks from the collision on the left side of its bow section.
According to US Navy personnel, the damaged destroyer was heading towards the Yokosuka Naval base, located about 50 km southwest of Japan's capital of Tokyo.
Neither of the vessels involved in the collision were in danger of sinking, according to the Japan Coast Guard.
