Japanese and American planes, boats and helicopters have been deployed but have so far failed to find the missing crew.
A Philippine-registered container ship struck the USS Fitzgerald destroyer in the early hours of Saturday morning.
Three people aboard were medically evacuated by air, including the USS Fitzgerald’s commanding officer.
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.
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.The Navy ship’s commanding officer, Cdr Bryce Benson, is in a stable condition after being transferred by helicopter to US Naval Hospital Yokosuka, according to Navy officials. Two others were flown to hospital, and were said to be awake and under observation.
The area where the collision took place is extremely busy, with shipping heading in and out of Tokyo bay.
However, the USS Fitzgerald is one of the most advanced warships in the world – with highly sophisticated radars systems.
At the moment the focus is on the search for the missing sailors. Later will come the investigation into how one of the world’s most sophisticated warships failed to avoid colliding with a 30,000-tonne cargo ship on a calm, clear night.