The bus, however, fell on the animal, killing it on the spot.
The incident took place near Kandhwar village under the Rampur Naikin police station limits, about 40 km from the district headquarters, a police official said.
Four persons who were seriously injured were taken to the Rewa Medical College Hospital while the others were undergoing treatment at Churhat and Rampur Naikin primary health centers.
The district superintendent of police Abid Khan said the bus was carrying more passengers than its capacity, and a probe had been ordered into the incident.