The van was coming from Sahiwal to Lahore, the capital of Punjab province, when its gas cylinder exploded, setting the vehicle on fire.
At least 12 passengers suffered severe burn injuries and were taken to Jinnah Hospital, where seven of them died, said a spokesman for the state-run rescue service.
The dead included two children and as many women.
The condition of four of the injured was critical, the spokesman said.
The explosion occurred due to a gas leak in the cylinder, he said.