Both buses plunged into water and, in both cases, the drivers are missing, police told CNN.
On Tuesday, a vehicle carrying mostly kindergarteners fell into a large drainage ditch near Amritsar in India's north, killing at least six students and injuring 14 others after the driver lost control of the vehicle.
Seventeen other students on the bus were unhurt.
It came just one day after 23 people died when their bus crashed into a pond in India's Bihar state, a district official said.
The private bus was carrying between 30 to 35 passengers, Giriwar Dayal Singh, Bihar's Madhubani District Magistrate, told CNN.
The victims included 11 children, six adult males and six adult females. Twelve people have been rescued so far.
Bus drivers missing or on the run
The second bus crash happened about noon local time near the village of Basaitha in Bihar.
The bus fell into a pond, which is about 20 meters deep, Nirmala Kumari, deputy superintendent of police in Bihar, told CNN.
Singh told CNN the driver of the bus is currently on the run. The driver from Tuesday's accident is also missing, according to police.
Rescue divers searched for victims and survivors in the Basaitha crash until 3 a.m. local time, said Kumari.
Officials are planning to remove water from the pond in order to search for more victims or survivors.