Rezaul Karim, assistant director of Inter Services Public Relation Directorate (ISPR), said the F-7 aircraft crashed around 2:50pm during an air exercise.
The accident left Pilot Wing Commander Arif Ahmed Dipu dead on the spot, he said.
Rezaul said the aircraft took off from Dhaka around 2:25pm.
Hailing from Iswardi of Pabna, Dipu was commissioned in Bangladesh Air Force in 1997. He had one son and daughter.
Wishing anonymity, an officer of Orunkhola police outpost said the plane burst into flames after it crashed into a Gozari forest inside Telki Firing Range.
It was not clear what caused the training aircraft to crash.