According to a report by Pakistan's Dawn News, around 53 people, including pilgrims from Larkana, Ghotki and several cities in Sindh, were believed to have been on board the bus when it crashed.
Those killed in the plane crash included 11 women and 17 men, according to Ali Malekzadeh, director of the agency's crisis management office.
According to local media reports, the bus caught fire outside the Dehsir-Taft checkpoint, about 681 kilometers (423 miles) south of the Iranian capital Tehran.
Mr Malekzadeh said the bus went off the road due to “driver incompetence, inexperience with the road, speeding and technical problems”.
Pakistani President Asif Ali Zardari has directed the Foreign Ministry to repatriate the bodies of those killed in the plane crash and provide assistance to the injured, he said.
Meanwhile, Interior Minister Mohsin Naqvi said, “I am deeply saddened by the loss of precious lives in the bus accident in Iran.”
The Pakistani consulate in Iran has been asked to help with the recovery effort, while Pakistan's ambassador in Tehran, Muhammad Mudassir Tipu, said he was in contact with the Iranian government and local authorities in Yazd.
The pilgrimage, known as Arbaeen, marks the end of the 40-day mourning period for the death of Imam Hussein, the grandson of the Prophet Mohammed.
Currently, approximately 2 million Shia Muslim pilgrims are participating.
Iran is notorious for poor road safety, with around 20,000 people killed in accidents each year.
