The Hindu pilgrims had gathered to take a dip in the Godavari river at the start of the Maha Pushkaralu festival.
The stampede occurred at 08:00am (02:30 GMT) in the Rajahmundry district.
Nearly 24 million pilgrims are expected to take part in the 12-day festival. Pilgrims believe that taking a bath in the river will rid them of their sins.
“The incident happened as the first set of worshippers were coming out of the river after taking a dip and then got in the way of others who wanted to be in the water at an auspicious time,” AFP news agency quoted senior police official A Srinivasan Rao as saying.
Deadly stampedes during religious gatherings are fairly common in India.
In October 2013, 115 people died during a stampede at a Hindu festival in the central state of Madhya Pradesh. Most were crushed after panic broke out on a bridge near the Ratangarh temple. Others drowned when they jumped from the bridge into river waters below.