Police said the plane crashed in the remote area of the southeastern district's Lohagara around 2:15pm on Tuesday.
"An air force plane, used for training purposes, crashed in the remote area of Bara Hatia's Faridghona," Lohagara police OC Md Shahjahan told bdnews24.com.
The Inter Services Public Relation Directorate or ISPR confirmed the incident and said the pilots on board were unharmed.
Wing Commander Nazmul and Squadron Leader Quamrul, who were on board, parachuted to safety, a Bangladesh Air Force officer told bdnews24.com, asking not to be named.
The pilots were transported from the crash site in an air force helicopter in the afternoon, locals said.
The plane had taken off from BAF Base Zahurul Haque in Chittagong at 2pm.
It crashed on a lychee farm owned by one Foez Ahmed at Ward -2 of Faridghona.
Local journalist Abu Taher who was in the farm area saw the pilots coming down using parachutes. "One of them was stuck in a tree and had to be rescued."
ISPR Assistant Director Nur Islam said the aircraft was a Yak-130, which was inducted into the Bangladesh Air Force in 2015.
He, however, could not say what caused the aircraft to crash.
Bangladesh had signed a deal with Russian state arms export agency Rosoboronexport to buy 16 Yak-130 trainers developed by the Irkut Corporation.
The deal was signed in 2013, according to Rosoboronexport head Anatoly Isaikin in an interview with Russia's ‘Kommersant’ newspaper.