The other two were being treated for lacerations and bruises, while other injured were being assessed aboard the ship, it said.
Search and rescue efforts by US and Japanese aircraft and surface vessels were continuing for the seven missing sailors, the Navy said. Their names are being withheld until the families have been notified, it said.
Benson took command of the Fitzgerald on May 13. He had previously commanded a minesweeper based in Sasebo in western Japan.
Unclear What Happened
It was unclear how the collision happened. "Once an investigation is complete then any legal issues can be addressed," the 7th Fleet spokesman said.
The Fitzgerald suffered damage on her starboard side above and below the waterline, causing "significant damage" and flooding to two berthing spaces and other areas of the ship, the Navy said. The flooding was later stabilised, but it was uncertain how long it would take to gain access to those spaces once the ship is docked, to continue the search for the missing, it said.
Back in Yokosuka, divers will inspect the damage and develop a plan for repairs, the Navy said.
The ship was able to operate under its own power with limited propulsion, the Navy said. The Japanese Coast Guard said separately the Fitzgerald was towed back to Yokosuka by a tugboat at about 3 knots.
Part of an eight-ship squadron based in Yokosuka, the Fitzgerald had in February completed $21 million worth of upgrades and repairs.
Japan's Nippon Yusen KK, which charters the container ship, ASX Crystal, said in a statement it would "cooperate fully" with the Coast Guard's investigation of the incident. At around 29,000 tons displacement, the ship dwarfs the 8,315-ton US warship, and was carrying 1,080 containers from the port of Nagoya to Tokyo.
None of the 20 crew members aboard the container ship, all Filipino, were injured, and the ship was not leaking oil, Nippon Yusen said. The ship arrived at Tokyo Bay around 5:00 pm (0800 GMT), sailing under its own power, the Coast Guard said.
The waterways approaching Tokyo Bay are busy with commercial vessels sailing to and from Japan's two biggest container ports in Tokyo and Yokohama.
International maritime rules for collision avoidance do not define right of way for any one vessel, but provide common standards for signaling between ships, as well as regulations on posting lookouts.
Japan's public broadcaster NHK showed aerial footage of the Fitzgerald, which had a large dent on its right, or starboard, side. Images broadcast by NHK showed it had been struck next to its Aegis radar arrays behind the vertical launch tubes.
Such incidents are rare.
In May, the US Navy's USS Lake Champlain collided with a South Korean fishing vessel but both ships were able to operate under their own power.
The 7th Fleet commander, Vice Admiral Joseph Aucoin, thanked the Japanese Coast guard in a post on the fleet's Facebook page, adding: "We are committed to ensuring the safe return of the ship to port in Yokosuka."