The bus was on its way to Indupur in Kendrapara district from Cuttack and was packed with passengers because of the limited bus service to the area.
Among those injured, four seriously injured were admitted to the SCB Medical College and Hospital in Cuttack and 26 taken to Gopalpur area hospital.
Fire tenders from Kuanpal and Chandikhole reached the spot and rescued the victims from the bus with help of local people. The accident took place at about 2 pm when the driver of the bus was trying to give way to an oncoming vehicle. Driver, conductor and helper of the bus fled from the scene soon after the mishap, police said.