The accident was reported around 10 am on Friday.
"The driver sustained injuries on hand, but the prisoners were taken to safety unhurt," Sub-Inspector of Tejgaon Industrial Police Abu Zafar Manik told bdnews24.com.
“While moving down from the flyover, the van turned 360 degrees and rolled over,” he said.
The prisoners were being taken to Kashimpur Jail from Dhaka Central Jail in Keraniganj, he added.
Driver Kamal told reporters: "The van suddenly jerked while moving downwards off the flyover, and then I lost control."
Traffic was suspended on the flyover but soon returned to normal after the van was removed by a wrecker.
The inmates are currently kept at the Tejgaon Industrial Police Station. They will be transferred to Kashimpur once a new van arrives, said the inspector.
The accident has created a scratch mark right in the middle of the lane of the flyover.