Seven other children were injured in the blaze which destroyed the vehicle.
The van was carrying 24 children to a private school in Gujrat, about 112 kilometres (70 miles) north of the eastern city on Lahore, when it caught fire, local police chief Dar Ali Khattak told AFP.
“The fire erupted in the vehicle when the children were only a few kilometres from their school,” he said.
The blaze was apparently caused by a spark when the driver of the dual-fuel van switched from gas to petrol, he said, adding that the fuel gas cylinder was intact.
The children were aged between five and 15 years old, he said, adding that a female teacher also died.
Another police official, Abid Khan, said the driver fled after the fire.
Five of the injured children were in serious condition, hospital officials said.
Vehicles in Pakistan mostly run on both petrol and natural gas.
Pakistan has one of the world’s worst records for fatal traffic accidents, blamed on poor roads, badly maintained vehicles and reckless driving.