While one of the deceased, identified as Uttam Jena, was a school teacher, the other was Madan Hantal, the police said.
After preliminary treatment, the injured were shifted to Jeypore and Koraput hospital as condition of five of them were serious.
The incident took place around 1 pm after one of the front tyres of the bus burst near Siribeda situated at a distance of about 60 km from here.
Chief Minister Naveen Patnaik condoled the death and announced Rs 2 lakh ex-gratia each to the next of the kin of the deceased persons. Patnaik also announced free treatment for the injured.