The accident occured around 9 pm on Barabati bridge on National Highway-16, when the bus with 40 passengers was en route to Kolkata from Puri.
Jajpur's Superintendent of Police, a team of doctors, and other district administration officials reached the accident spot to supervise the rescue operations.
The fire personnel rescued the injured using gas cutters.
Chief Minister Naveen Patnaik condoled the deaths and announced a compensation of Rs. 3 lakh each for the families who lost a loved one.