The fighter jet went missing at around 7:30 pm (AEST) as it was flying some 135 kilometres east of Misawa, northeastern Japan, a ministry spokeswoman said.
The F-35s are shipped to Japan by Lockheed Martin and assembled by Mitsubishi Heavy Industries Ltd at a plant near Nagoya in central Japan.
Japan sent air and naval forces to the area for the search, he added.
Japanese military officials told local media outlets that no problems with the jet were reported before it disappeared.
The stealth fighter, which has been beset by cost overruns and delays, has a price tag of around $100 million each. The pilot had 3,200 hours of flight time, with 60 hours on the F-35, the official said.
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The aircraft was less than a year old and was delivered to the ASDF in May last year, the ASDF spokesman said.
If the flight had crashed it would become only the second time an F-35 has gone down since it becoming operational 20 years ago.
The JASDF stood up its first F-35A fighter squadron, the 302nd Squadron, part of the service's 3rd Air Wing, at Misawa Air Base last month. It was also the first crash of an A version of the fifth-generation fighter created to penetrate enemy defences by evading radar detection. The Air Self Defense Force (ASDF) confirmed the wreckage was that of the missing jet. The first one occurred on September 28, 2018 when a U.S. Marine F-35B Lightning II crashed near Beaufort, South Carolina.
The Pentagon said it was monitoring the situation.
Japan has started deploying the expensive US -made F-35s since last year, part of its plan to bolster its defense spending and weapons capability in the coming years to counter potential threats from North Korea and China. Lockheed Martin also makes a C version of the fighter created to operate off carriers.