Local police said a jeep, on its way from Chhattarpur district in northeast Madhya Pradesh to Bhopal, the state capital, was swept away in the Lehdara Nullah, a swollen rivulet.
Five of the eight passengers were drowned, police said.
In another incident, a bus carrying people to attend a wedding party, was washed away in the floods. Fifteen people, including the driver and conductor, went missing.
The army is assisting the civil administration in rescue and relief operations in the northeastern part of the state.
Road and rail traffic was affected by the flooding of rivers and rivulets in many places. Two passenger trains had been suspended as the tracks remained submerged, an official spokesman said. Telecommunication, water supply and electricity transmission remained disrupted as well.
Seven districts of the state received heavy rains in the past three days. Katni District received nearly 90 cm of rainfall in the past four days and 300 people were evacuated to safety.
The flood in neighboring Gujarat Pradesh has claimed 150 people and made 400,000 homeless in the past week.