Fifteen people were rescued by local fishermen.
The ill-fated boat was being operated by a private company and was said to be on a trial run.
National Disaster Response Force (NDRF) teams and Krishna district authorities have launched a massive search and rescue operation to trace the missing people.
Tourism Minister Bhuma Akhila Priya ordered an inquiry into the incident and directed her department officials to ascertain whether the boat operator had requisite permissions.
operation at krishna river in AP pic.twitter.com/Sn3fqOJ28b
— NDRF (@NDRFHQ) November 12, 2017
The incident occurred when the boat set off for Pavitra Sangamam at Ferry village near Vijayawada from Bhavani Island, the police said.
"The boat was overloaded with 38 people and most of them were not provided life jackets. It capsized near a curve as it approached the Pavitra Sangamam point and most of the people were trapped underneath and were killed," an Assistant Commissioner of Police said.
Most of the passengers were said to be members of the Ongole Walkers Club in Prakasam district while some were from Nellore who were on a visit to Vijayawada.
Local fishermen at Ferry swung into action immediately and rescued 15 passengers.
Later, 16 bodies were fished out of the river.
Two teams each comprising 30 NDRF personnel, a 45-member team of the State Disaster Rescue Force (SDRF) and 60 members of the Disaster Response and Fire Services Department have been roped into the rescue operation.
Chief Minister N Chandrababu Naidu, Deputy Chief Minister (Home) N China Rajappa, Opposition leader Y S Jaganmohan Reddy, state BJP president K Hari Babu and others expressed grief over the incident.
China Rajappa, who was supervising rescue operations at the accident spot, announced an ex-gratia payment of Rs 5 lakh each to the kin of the deceased.
Two persons, who were rescued from the tragedy, complained of sickness and were shifted to a government general hospital in Vijayawada, the officials said.
Pradesh Congress Committee president N Raghuveera Reddy visited the accident spot and later the hospital.
One of the deceased was identified as Prabhakar Reddy, a former president of the BJP Prakasam district unit.