Police official Raju Manandhar said the victims were Hindu pilgrims returning from a visit to a local temple in Baraha village, about 250 miles (400 kilometers) southeast of the capital, Katmandu.
Police rescuers and local villagers rushed to the scene to help and managed to rescue several of them.
Most of the victims drowned in the canal, while the injured suffered only minor wounds and scratches, the police official said. Those killed were 16 women, one man and a child.
The driver fled the scene, and police were investigating the cause of the accident.
It is common in impoverished areas for people to travel on trailers pulled by tractors that are generally used for farming. Both vehicles and roads are poorly maintained in many parts of Nepal.
