The driver, who was headed towards the city of Dera Ghazi Khan in eastern Punjab province, was driving on Taunsa Road when the incident happened.
Emergency workers rushed to the scene and transported victims to a nearby hospital, according to Sher Khan, who was in charge of the rescue team. A total 33 people are said to have died.
Mr Khan said the passengers were travelling to their home district of Rajanpur to celebrate the upcoming Eid al-Adha feast.
The religious event is the second of the two Eid festivals in the calendar and celebrates and honours the story of Prophet Ibrahim - known to Christians as Abraham.
Video footage and pictures shared on social media showed rescuers trying to pull out bodies from the impacted bus while others show them wrapped up and lying on the ground.
Pakistan's Information Minister Fawad Chaudhry expressed his condolences on Twitter and advised public transport drivers to be more careful of the lives of the people they have been entrusted with.
"When will we as a nation realize that the violation of traffic rules is fatal," he said.
Deadly accidents are common in Pakistan due to poor road infrastructure and disregard for traffic laws.