How the crash happened was not yet clear, while the names of those aboard were being withheld.
Eight people have been found though their condition was not clear, Japan's defence minister said.
The aircraft was taking part in a joint Japan-US naval exercise that is due to end on 26 November.
A propeller powered transport plane, the C-2 Greyhound carries personnel, mail and other cargo from mainland bases to carriers operating at sea.
The type has been in operation for more than five decades and is due to be replaced by the long-range tilt-rotor Osprey aircraft.
The US 7th Fleet said a search and rescue operation had been launched.
"Personnel recovery is underway and their condition will be evaluated by USS Ronald Reagan medical staff," a statement read.
The Reagan was operating in the Philippine Sea when the crash took place, at about 2.45pm local time.
The 7th Fleet has had two fatal accidents in Asian waters this year, leaving 17 sailors dead and prompting the removal of eight top Navy officers from their posts, including the 7th Fleet commander.
The USS John S McCain and an oil tanker collided near Singapore in August, leaving 10 US sailors dead. Seven sailors died in June when the USS Fitzgerald and a container ship collided off Japan.
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