The van was carrying passengers from Karachi to Hyderabad city when it struck an object and careered off the road late Saturday.
"The death toll in the unfortunate accident has reached 15," Owais Shah, the transport minister of Sindh province, told AFP.
Five other people were injured, three of them critically, he said.
Most of the bodies were burned beyond recognition, said Faisal Edhi, head of the non-profit Edhi Foundation which runs the morgue the bodies were taken to.
Investigators were looking to see if a natural gas cylinder aboard the bus had contributed to the inferno.