Japanese Defense Minister Takeshi Iwaya said that the MoD "will put all our efforts to save the life [of the pilot] first", according to The Japan Times.
No problems with the aircraft were reported before it went missing, NHK reported.
The ASDF's radar lost track of the jet when it was about 135 km east of Misawa Air Base in the prefecture, Japan Times reported.
That's about all that's know thus far, but if the plane is found to have crashed, it would be the second such incident for an F-35.
JASDF aircraft, along with Japan Maritime Self Defense Force (JMSDF) and Japan Coast Guard (JCG) vessels, have begun a search mission.
"If one of Japan's F-35s is sitting at the bottom of the Pacific, we are probably about to see one of the biggest underwater espionage and counter-espionage ops since the Cold War".
Last August, the nonprofit Project On Government Oversight (POGO) said that senior officials developing the F-35 Joint Strike Fighter for the U.S. armed forces - the most expensive military program of all time - are covering up unsafe flaws in the plane instead of fixing them.
A U.S. military F-35B crashed near the Marine Corps Air Station Beaufort in SC in September, prompting a temporary grounding of the aircraft.
Japan had only stood up its first F-35A squadron at the end of last month, with the 302nd Hikotai established in Misawa with 13 F-35As following its transfer from Hyakuri, north of Japan's capital Tokyo, where it had been operating the Mitsubishi F-4EJ Phantom II. Lockheed Martin also makes a C version of the fighter created to operate off carriers.
Japan has been deploying F-35s, which cost at least $90m (£68m), to replace its ageing F-4 fighter jet.
The F-35A in question was engaging in anti-fighter combat training with three other F-35A jets.
In the Pacific, South Korea and Australia have joined Japan in acquiring the jets.