Images from the scene in the northern city of Prajagai showed rescuers helping the wounded as police tried to manage the huge crowds.
It was not clear immediately what caused the panic of the festival, where the devoted from all over India had gathered to bathe at the merger of Ganges, Yamuna and the mythical rivers Saravati. Press Trust of India cites authorities who said wounded people were sent to hospital.
The Maha Cumbus Festival, held every 12 years, began on January 13 and is the largest religious gathering in the world. Authorities expect more than 400 million people to throw overall worship over the next six weeks.
In order to accommodate tens of thousands of holy people, pilgrims and tourists visiting the festival, the authorities have built a scattered city on a tent on river shores.
It is equipped with 3,000 kitchens and 150,000 toilets, and also has roads, electricity and water, communication towers and 11 hospitals.
About 50,000 security officers are located in the city to maintain a law and order and to manage the crowds. Stampedes are relatively common around Indian religious festivals, where large crowds gather in small regions.