The US Navy said rescue workers found the bodies on Sunday after gaining access to damaged parts of the ship.
It said they will be taken to a Japanese hospital to be identified.
The incident took place some 56 nautical miles (104km) south-west of the Japanese port city of Yokosuka, at about 02:30 local time on Saturday (17:30 GMT Friday).
The Navy ship's starboard side was heavily damaged in the collision, but the vessel later managed to slowly return to its base in Yokosuka, with the assistance of US navy tug boats.
At a press conference in Japan on Sunday, Vice-Admiral Joseph P Aucoin said he would not say how many remains had been found so far. Families of the sailors are being notified, he said.
"This loss is something we all feel," he said.
Marine traffic records suggest the ACX Crystal, a 222-metre (730ft) Filipino-flagged container ship, made a sudden U-turn roughly 25 minutes before the crash. It is not known why it changed course.
Similar records for the USS Fitzgerald are not publicly available.
Japanese broadcaster NHK said the collision in the middle of the night led to the flooding of the crew's sleeping quarters.
Japan's coastguard said the ACX Crystal had a gross tonnage of just under 30,000, about three times that of the USS Fitzgerald.
It sustained lighter damage to its port bow.
The Associated Press agency said there were no injuries reported among the 20 Filipino crew members on board the container ship.
More about: #USnavy