The F-7BGI aircraft crashed on the Milestone School and College in Dhaka's Uttara area, where children were present, a fire official said.
Television footage showed a fire and smoke billowing from the site of the crash.Â
Khaleda Khatun, an official on duty at the Fire Service and Civil Defence control room, said nine fire engines were working to extinguish the fire.
"We cannot provide an exact number of casualties at this moment as the rescue operation is on, but it is feared many," she told DPA.
At least 20 injured people were transported to hospitals, she said.
The Bangladesh Army's public relations office confirmed the downed aircraft belonged to the Air Force.
Muhammad Yunus, head of Bangladesh's interim government, said "necessary measures" would be taken to investigate the cause of the accident and "ensure all kinds of assistance".
"The loss suffered by the Air Force...students, parents, teachers and staff, and others in this accident is irreparable," he said.
Local newspaper Prothom Alo said initial reports indicated the plane had crashed onto the roof of the college canteen. Reuters could not independently verify this information.
Monday's incident comes a little over a month after an Air India plane crashed on top of a medical college hostel in neighbouring India's Ahmedabad city, killing 241 of the 242 people on board and 19 on the ground, marking the world's worst aviation disaster in a decade.
with AP and DPA
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