The mishap occurred when the bus from Anandapur in neighbouring Keonjhar district was headed for Cuttack after a wedding ceremony, they said.
Fire brigade personnel of Jajpur Road rushed to the site and rescued the injured with assistance of the local people. The injured were first admitted to Area hospital in Jajpur Road and later four critically injured were shifted to SCB Medical College and Hospital in Cuttack after their condition deteriorated, police said.
The cause of the mishap is yet to be ascertained, the police said.