A number of people are also reportedly hurt, with one evacuated by helicopter.
The crash involving the Navy destroyer USS Fitzgerald happened 56 nautical miles (103km) south-west of the city of Yokosuka at about 2:30am local time (18:30 BST) on Saturday.
Japan's public broadcaster, NHK, showed aerial footage of the US ship with heavy damage on one side.
One injured sailor has been evacuated to hospital by the coastguard's helicopter.
In a series of tweets, the US 7th Fleet earlier said the USS Fitzgerald had experienced flooding in some areas, and the extent of injuries was being determined.
It said the ship was now on its way to Yokosuka - under its own power, but with limited propulsion.
The coast guard said the other ship carried a Filipino flag and weighed just under 30,000 tonnes.
The area where the collusion 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.
There will now be lots of questions about why its crew failed to avoid collision with a 200m (700ft) long container ship.
In a statement released on social media, US Navy operations chief Adm John Richardson said: "As more information is learnt we will be sure to share it with the Fitzgerald families and when appropriate the public. [...]
All our thoughts and concerns are with the Fitzgerald crew and their families."
