It was not immediately known whether the two crew members survived the crash.
The T-4 aircraft disappeared off the radar around 3:08 p.m. while flying near the city of Inuyama, Aichi Prefecture, where the lake is located, after leaving the ASDF's Komaki base in the neighbouring Aichi city of Komaki at 3:06 p.m.
Chief Cabinet Secretary Yoshimasa Hayashi, the top Japanese government spokesman, said in Tokyo that the plane crashed soon after taking off.
The Aichi prefectural police received emergency calls from around 3:10 p.m. reporting that a fighter jet had crashed into the lake, located some 10 kilometers north-northeast of the Komaki base.
No damage to houses or local residents has been confirmed, according to the Inuyama city government.
The aircraft was heading for the ASDF's Nyutabaru base in the southwestern prefecture of Miyazaki.
"We deeply apologise for causing great trouble," Defence Minister Gen Nakatani said. "We are fully committed to rescuing (the crew members)."
The SDF began a rescue mission, while police and fire authorities deployed an underwater drone and a diving team, respectively.
Makoto Matsuo, 33, a corporate employee from the Aichi city of Seto, said that he heard a thunderous noise twice while fishing on a boat on the lake at the time.
He said that the air smelled like fuel when he approached the crash site, adding, "There was a lot of debris floating on the surface of the lake."
A worker at a local restaurant heard from a person who was fishing at the lake that the aircraft had fallen straight into the lake.
[Copyright The Jiji Press, Ltd.]