The accident happened near the ancient city of Ayutthaya, a popular tourist attraction, although no foreigners were believed to be among the dead.
"There are 13 confirmed dead and 33 injured so far," said Udomsak Khaonoona, disaster prevention chief for the city which is 80 km (50 miles) north of Bangkok.
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"The boat tried to avoid another vessel and crashed into the concrete column of a bridge," he told AFP, adding that the passengers were local.
Around 100 passengers were believed to be on board the vessel, with four currently unaccounted for, Udomsak said.
Video footage posted by Khaosod TV showed desperate scenes as rescue workers scrambled to reach the stricken vessel, its stern partially under water.
Rescuers threw ropes to help people swim to land as others gave CPR to unconscious victims on the banks of the river.
Despite its wealth compared to regional neighbours and huge tourism sector, accidents are common on Thailand's public transport network. Safety regulations are often weakly enforced.
The country has one of the world's worst road traffic death rates, and crashes of speedboats operating between the popular southern tourist islands are also common.
The Chao Phraya, the main river that flows through Bangkok, is a key commuting artery, filled with often packed boats plying the waterways at breakneck speed.
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