Brazilian and Paraguayan officials said that 13 people had managed to swim ashore, but 11 are still missing and presumed dead.
The Paraguayan vessel, Dream of the Pantanal, sank during a heavy storm on the Brazilian border.
Officials said it was carrying 11 Paraguayan crew and 16 Brazilian tourists.
"Four teams comprising a total of 21 firefighters, including 14 divers, have been mobilised," a Brazilian rescue official told the AFP news agency.
Aldo Saldivar of Paraguay's National Emergency Secretariat said the tourists had been on a fishing expedition to the Pantanal.
The area, which stretches across areas of Brazil, Paraguay and Bolivia, is one of the world's largest freshwater wetlands.
The boat sank in a storm on Wednesday afternoon between the towns of Carmelo Peralta in northern Paraguay and Porto Murtinho, in Brazil's Mato Grosso do Sul state.
Most of the victims came from the same Brazilian town, in Parana state.
They had rented the boat and had spent 10 days together, fishing in the Pantanal area.
The boat capsized less than 48 hours before the planned end of the excursion.
The bodies of three Brazilian tourists have been retrieved after their boat capsized on the River Paraguay.