However, officials are yet to confirm any deaths caused by the stampede.
The festival kicked off earlier this month in the northern state of Uttar Pradesh.
Officials said the incident took place on Mauni Amavasya -- the most significant day of the festival. Local authorities had expected a record 100 million attendees.
Indian Prime Minister Narendra Modi termed the accident "extremely sad."
"My deepest condolences to the devotees who have lost their loved ones in this. Along with this, I wish for the speedy recovery of all the injured," Modi said.
He said the local administration is "engaged in helping the victims in every possible way."
The Maha Kumbh takes place every 12 years on the riverbanks in the city of Prayagraj. This year, it is being held from Jan. 13 to Feb. 26 and some 400 million people are expected to attend the festival.
Prayagraj, formerly Allahabad, is considered particularly holy to Hindus, as it is home to Triveni Sangam, the sacred confluence of the Ganges, Yamuna, and mythical Saraswati rivers.
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