Two others were hurt along with the USS Fitzgerald's commanding officer Bryce Benson, the military said in a statement.
"Two sailors, in addition to the commanding officer, have been medically evacuated from USS Fitzgerald to US Naval Hospital Yokosuka for lacerations and bruises," it added.
"There are seven sailors unaccounted for; the ship and the Japanese Coast Guard continues to search for them."
The collision between the US guided missile destroyer and the ACX Crystal took place off the coast of the Izu peninsula southwest of Tokyo, at about 2:30 am (local time), the US Navy and Japan's coastguard said.
Aerial television footage showed an apparent victim on a stretcher and a Japanese rescuer being pulled up to a helicopter hovering over the huge destroyer.
The coastguard has sent five vessels, two planes and a team of specially trained rescue personnel to the area, the spokesman said.
The 154-metre Fitzgerald is based in Yokosuka on the Izu peninsula and operates in the Pacific and the Sea of Japan (East Sea).
In a statement released on Twitter, US chief of naval operations Admiral John Richardson said: "As more information is learned we will be sure to share it with the Fitzgerald families and when appropriate the public.
Video by Japan's public broadcaster NHK showed heavy damage to the right side of the Fitzgerald just ahead of the control tower, and that the ship had taken on water.
An orange hose was visible on the ship's deck, with many crew members seen checking the damage.
NHK said the destroyer, piloted by two tugboats, was sailing to Yokosuka.
"The USS Fitzgerald suffered damage on her starboard side above and below the waterline. The collision resulted in some flooding," the Navy said.
A US defence official told AFP that "sailors are de- watering" flooded areas of the ship.
The footage meanwhile showed relatively light damage on the port bow of the ACX Crystal.
Twenty crew members were aboard the container and no one was injured, another Japanese coastguard spokesman said, adding that the vessel was separately sailing back to a Tokyo port.
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