The suspect, described by officials as a 25-year-old Bangladeshi man, was shot as special forces rushed the plane after it landed safely in Chittagong.
The 148 passengers and crew aboard the Bangladesh Biman flight BG147 were all rescued unharmed, officials said.
But the suspected hijacker was injured and died shortly after being arrested, army spokesman Major General Motiur Rahman told reporters.
"He is a Bangladeshi. We found a pistol from him and nothing else," Rahman said.
All the passengers aboard were evacuated after the airport was sealed off by Army, Navy and elite police, Presstv reported.
Air Vice Marshall Mofid, who goes by one name, said he then kept the accused man busy talking on the phone while special forces units prepared for the dramatic raid.
"He demanded to speak to our Prime Minister (Sheikh Hasina)," Mofid said.
"He claimed he had a pistol, but we are not sure yet whether it is an actual gun or a fake."
The country's civil aviation chief, Nayeem Hasan, earlier said the suspect had claimed to have a bomb aboard the flight.
"From the talks and dialogue we have with him, it seems he is psychologically deranged," Hasan said after the man was arrested.
Another army spokesman, Abdullah Ibne Zaid, said the would-be hijacker allegedly claimed to have a gun and a bomb strapped to his chest.
"The army's special forces conducted the operation and the armed man has been neutralized.
The situation at (Chittagong's) Shah Amanat International Airport is very much under control of the Bangladesh Army," he said.
An investigation would be carried out to determine whether security lapses had occurred, he added.
Bangladesh, a Muslim-majority nation of 165 million, has grappled with homegrown extremism, with extremist outfits murdering atheist bloggers and progressive activists in recent years.
In a deadly attack claimed by Daesh group in 2016, militants killed 22 people including 18 foreigners at an upmarket cafe in Dhaka popular with Westerners.
That attack prompted a swift crackdown by Prime Minister Hasina, with hundreds of suspected militants and their sympathizers arrested or killed in raids across the country.