The bus was carrying pilgrims to the shrine city of Karabla to mark the festival of Arbaeen, when its brakes failed and it flipped over yesterday evening, the ISNA news agency.
Some 2.5 million Iranians are expected in Karbala this month for Arbaeen, which marks the 40th day after the death in the seventh century of Imam Hussein, one of the pivotal figures of the Shiite faith.
An estimated 16,000 people were killed in road accidents in Iran in the year to March 2016.