The mishap took place near Deulijhari when the bus from Boudh to Athamallik fell from a bridge at Puruna Manitri, DGP K B Singh said.
While 16 persons, including four women, were killed, 30 others sustained serious injuries in the accident, Singh said.
The injured were admitted to a hospital at Athamallik where the condition of many was stated to be critical, said Angul District Collector Anil Kumar Samal who rushed to the spot to supervise rescue operations.
Expressing shock over the mishap, Chief Minister Naveen Patnaik directed the district administration and police officials to take immediate steps for medical treatment of the injured persons.
The chief minister directed that the injured be provided medical treatment free of cost, officials said.
Several students of Athamallik college were also travelling in the bus, they said.
It was not immediately clear as to how the bus fell off the bridge, but the driver appeared to have lost control over the vehicle, they said.