The bus was carrying passengers from Thon Buri district of Bangkok, to Wat Wang Khanai Tayikaram in Tha Muang district for Buddhist rites.
The bus overturned about 9.30am in Tha Maka district.
The police and rescue volunteers said they found the bus lying on its right side, blocking both lanes of the road. Motorists were directed to other routes.
Rescuers said 40 injured passengers were sent to two nearby hospitals. Two passengers, Jinda Yukongphan, 62, and Wiphanrat Jongnarungsin, 61, died inside the bus. A third person died in hospital.
Sirichai Phetkaew, 17, a bus boy, said the double-decker bus, belonged to Heng Heng Tour, suddenly overturned. He could not provide more details of why it overturned as he was not fully awake, rescuers said.
Police suspect the driver fell asleep at the wheel. He was believed to be unfamiliar with the road and was driving too fast.