The suspect, who reportedly warned he had a pistol, was killed when security forces stormed the plane after it made an emergency landing in Chittagong.
All 148 passengers and crew on board the Biman Bangladesh Airlines Flight BG147 disembarked safely.
It is not yet clear why the suspect may have attempted to hijack the plane.
Army officials said the man, believed to be aged 25, was initially wounded when shots were fired on Sunday but died shortly afterwards, AFP news agency reports.
“We tried to arrest him or get him to surrender but he refused and then we shot him,” Maj Gen Motiur Rahman told reporters.
“He is a Bangladeshi. We found a pistol from him and nothing else,” he added.
Earlier reports suggested that the suspect may have been mentally ill and had demanded to speak with Bangladeshi Prime Minister Sheikh Hasina, who was visiting the coastal city of Chittagong.
Staff on board the flight raised concerns after the man was said to have been acting suspiciously and indicating intent to hijack the plane, Reuters news agency reports, quoting airline officials.
The aircraft was immediately cordoned off when it landed at the Shah Amanat International airport in Chittagong as officers attempted to talk to the suspect.
Images posted on social media showed crowds of people on the tarmac at the airport with the Boeing 737-800 aircraft visible in the background.
The flight was originally scheduled to arrive in Dubai on Sunday evening after departing from Dhaka.