The accident happened in Khuzdar, a district in Baluchistan province, before dawn on Friday, local police official Hafeez Ullah Mengal said.
Rescuers transferred the deceased and injured to military and government hospitals, he added.
Imam Bakhsh, one of the wounded passengers, told The Associated Press that passengers had frequently warned the driver to be more careful.
He blamed the driver for the accident, saying he was enjoying music and driving recklessly.
Imran Ahmad, an official with the Levies security force said driver negligence apparently caused the accident, but that officers were still investigating.
The pilgrims were returning to Dadu, a district in the neighbouring southern Sindh province, after visiting a shrine of a Sufi saint.
Bashir Ahmed, a deputy commissioner in the Khuzdar district, said the driver lost control on a sharp turn.
He said the bus was overcrowded and several pilgrims were also sitting on its roof when the accident took place.
Mr Ahmed said some of the injured were listed in critical condition, including the bus driver.
“There is not a single passenger who does not have an injury because of the bus accident," Mr Ahmed told the AP by phone.
Traffic and rail accidents are commonplace in Pakistan, partly because of the poor road infrastructure and traffic laws.
Last month, another bus overturned on a highway in the southern district of Sukkur, killing 13 passengers and injuring 29 others.
The latest bus accident happened days after at least 65 passengers were killed in a horrific collision of two trains in the southern town of Ghotki in the Sindh province.
The incident took place on a dilapidated railway when an express train collided into another that had derailed minutes earlier on Monday.
Additional reporting by Associated Press