The van was transporting 37 old and new prisoners back to the jail after their court appearance in Dhaka city, said Shah Zaman.
All the injured were from the prison van, he said.
Critically injured prisoners Atikur, 22, Atul, 24, Munna, 25, Murad, 40, and Rumi, 42, were admitted to Dhaka Medical College and Hospital, he added.
Besides 12 other prisoners were given primary treatment at the jail hospital while the two policemen were taken to Rajarbagh Police Lines Hospital.
The OC did not provide details about what happened to the bus.