The destroyer collided with the container ship about 56 nautical miles (104km) south-west of Yokosuka.
Aerial images showed heavy damage to the Navy ship's starboard side after the collision at about 02:30 local time on Saturday (17:30 GMT Friday).
The collision occurred near Yokosuka, a Japanese port city that is home to the US 7th Fleet, which comprises up to 80 submarines and ships and including the USS Fitzgerald.
It is unclear where the 154-metre (505ft) guided missile destroyer ship was heading at the time.
The ACX Crystal, a 222-metre (730ft) Filipino-flagged container ship, was travelling between the Japanese cities of Nagoya and Tokyo.
Marine traffic records suggest the ACX Crystal made a sudden U-turn roughly 25 minutes before the collision with the USS Fitzgerald. It is not clear why it changed course.
Marine traffic records suggest it was travelling at 14.6 knots (27km/h) at the time of the collision.