The passenger bus from Bhubaneswar was proceeding towards Sinapalli in Nuapada when the mishap took place near Puintala, three km from here, in the early hours, police said.
As the bus caught fire soon after hitting the tree, five passengers were charred to death while 38 others suffered multiple injuries, he said.
The injured were admitted to Bolangir District Headquarters Hospital. Two of them were later shifted to VSS Medical College and Hospital at Burla in a critical condition, police said.
The driver and conductor of the bus fled from the spot after the mishap.