The locally-made Brave Eagle went down after taking off from Chih Hang Air Base in southern Taitung county at 8:40 am, the air force said in a statement.
The pilot, identified as Major Lin, was rescued and taken to hospital where he was in "good health" with no injuries, it said.
The air force said the jet suffered "dual engine failure" but a special task force would investigate "to clarify the cause and ensure training safety".
It said all Brave Eagle advanced jet trainers (AJT) have been grounded for safety checks following the crash.
Taiwan has a homegrown defence industry and has been upgrading its equipment, but it still relies heavily on US arms sales to bolster its security capabilities against a potential Chinese attack.
China claims Taiwan as part of its territory and has threatened to use force to bring it under its control.
The Brave Eagle was made by Taiwan's Aerospace Industrial Development Corp and had its first test flight in 2020.
The pilot of the aircraft that crashed Saturday had 183 flying hours, the air force said.
In September, Taiwan temporarily grounded its fleet of Mirage 2000 fighters for safety checks after a jet crashed into the sea.
Taiwan's Mirage 2000 fighters were purchased in 1992 from France in an arms deal that angered China.
They are still a core component of the island's ageing fleet, which also includes F16 fighter jets from the United States, and locally built Indigenous Defence Fighters.
Taiwan's military is under pressure from China, which has in recent years ramped up incursions by fighter jets and warships around the island -- actions that military experts dub as grey-zone tactics that serve to exhaust the island's armed forces.
In the 24-hour period ending 6:00 am on Saturday, 19 Chinese military aircraft, eight naval vessels, one official ship and one balloon were detected around the island, Taiwan's defence ministry said.
Speaking to reporters on Saturday, President Lai Ching-te said he hoped the opposition-controlled parliament would remedy the sections of the defence budget that have been frozen or cut to show "our full support for the military".
"In the face of China's threats, the military is bravely protecting our country".
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