The Royal Vasishta vessel was carrying 61 people - 50 passengers and 11 crew members, all of them Indian nationals - when it capsized on the Godavari River on Sunday, Andra Pradesh state's Home Minister Mekathoti Sucharita said.
A search operation was under way, with rescue teams including divers and a helicopter scouring the river to find the missing people, a senior police official said.
Twenty-four people have been rescued so far, while 25 others are missing, Sucharita said.
The accident occurred near Kachuluru village in East Godavari district, 380 kilometres (236 miles) east of the state's capital, Hyderabad. The boat was heading from Singanapalli to Papikondalu, a famous tourist spot.
Sucharita said tour boats had been barred from operating on the route following the recent flooding of the river and it was not clear how the boat that capsized had managed to take out the tourists.
"Stern action will be taken against the culprits," she told the Associated Press news agency.
Apart from tourists, residents in the area depend on boats and ferries to travel between villages on the banks of the Godavari.
The river had been flowing quickly for a week, local media said, adding that the boat was run by the state government.
Overcrowding and poor safety checks often cause boat accidents in India, especially during the annual monsoon rains when rivers are swollen.
Last week, a dozen people died in Bhopal city in central India after two boats capsized during a ceremony to immerse an idol of Hindu god Ganesha into a river.
In May 2018, 30 people were killed when a similar boat carrying local people capsized not far from the scene of Sunday's accident.
A few months later, a boat carrying 80 tourists caught fire when a cooking gas cylinder exploded, but there were no casualties.
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