A training aircraft belonging to the Bangladesh Air Force crashed onto a school campus in northern Dhaka on Monday, killing at least one person and injuring several others, the military and a fire official said.

The Bangladesh Army's public relations office confirmed in a brief statement that the downed F-7 BGI aircraft belonged to the Air Force.

Fire official Lima Khanam stated by phone that at least one person died and four others were injured, though she did not provide further details.

The jet crashed onto the campus of Milestone School and College in Dhaka's Uttara neighbourhood, where students were taking tests and attending regular classes.

Television footage showed fire and smoke billowing from the crash site.

Jamuna TV reported that at least 13 people, including students, were injured.

The Bengali-language daily paper Prothom Alo said most of the injured were students who had sustained burns and that at least 20 people were taken to a hospital.

Parents and relatives panicked at the scene as rescuers, using tri-cycle rickshaws or whatever was available, transported the injured to hospitals.

Rafiqa Taha, a student at the school who was not present at the time of the crash, told the AP by phone that Milestone School and College has around 2,000 students and offers classes from elementary to 12th grade.

"I was terrified watching videos on TV," said the 16-year-old student. "My God! It's my school."