The USS Ronald Reagan joined two other aircraft carriers earlier this month near the Korean Peninsula in a show of force to North Korea as tensions between the United States and the rogue nation continue to ratchet up.
The Nov. 16-26 joint exercise in waters off Okinawa has been described by the Navy as the "premier training event" between the USA and Japanese navies, created to increase defensive readiness and interoperability in air and sea operations.
The C-2 is a twin-engine cargo plane created to transport people and supplies to and from aircraft carriers.
The U.S. Navy says an aircraft with 11 people on board crashed in the Pacific Ocean.
The Defense Ministry says it had no information on their condition.
The 7th fleet, based in Japan, said a search and rescue operation was under way.
The search for the remaining three is continuing.
It was operating in the Philippine Sea when the crash happened at 2.45pm local time (approximately 5.45am GMT).
The cause of crash is unknown and the names those onboard are being withheld while next of kin are notified, the US Navy said in a statement.
Japanese Minister of Defense Itsunori Onodera told reporters that U.S. Navy officials had informed him the crash could be the result of engine problems. The Reagan is home-ported at the USA naval base in Yokosuka, Kanagawa Prefecture.
Trump is spending Thanksgiving at his Mar-a-Lago resort in Florida.