The National Disaster Response Force personnel joined divers in the rescue operation, which was hampered due to the darkness after sunset.
Local fishermen swung into action and rescued 15 passengers, the Press Trust of India reported.
"Boat carrying approx.35 people capsized at Krishna River, Ferry Ghats, Krishna district AP". "Many of the tourists got trapped under the overturned boat and died of suffocation", said one of them.
The incident occurred when the boat set off for Pavitra Sangamam at Ferry village near Vijayawada from Bhavani Island, the police said. In a separate incident, at least six people had drowned in river Ganga in Bihar's Maranchi.
The state's tourism minister ordered an inquiry into the incident while Chief Minister Chandrababu Naidu expressed his condolences on Twitter.
Home Minister N. Chinnarajappa, who rushed to the site, said 16 bodies had been recovered while the search was on for the missing.
National Disaster Response Force personnel are now performing rescue operation.
A search operation is now underway, state DGP Sambha Shiva Rao said.
Andhra Pradesh Congress committee president N Raghuveera Reddy visited the accident spot and later the hospital.