The bridge is about 50m (165 ft) high.
About 33 to 40 people were on board the ill fated bus and the survivors are said to be seriously injured.
The bus was travelling through the northern province of Phetchabun when it plunged off the bridge, Police said. Khun Pha Muang is described as a bridge with some of the highest pillars in Thailand.
“We believe the bus driver fell asleep,” local police commander Sukit Samana told the Agence France-Presse news agency.