An exploding gas canister is reported to be the cause as the train was engulfed in flames.
The blaze is thought to have spread to at least three carriages.
Local reports suggest many of the victims died as they tried to jump off the burning train.
Another 39 people have been injured, according to the BBC, amid fears the death toll may still rise.
Cooking stoves are a common problem for train services in Pakistan, according to minister Sheikh Rashid Ahmed.
He added: “Two cooking stoves blew up. They were cooking, they had (cooking) oil which added fuel to fire.”
District deputy commissioner Jamil Ahmed said some of the victims could not be identified due to the burning, and they would need to use DNA to find out who had died.
Prime Minister Imran Khan said he was “deeply saddened by the terrible tragedy” on Twitter, adding that he had ordered an “immediate inquiry”.
The horrific accident occured near the small town of Rahim Yar Khan in the south of the Punjab province.
The train was travelling from Karachi in the south of the country to Rawalpindi in the north.