The accident occurred between Tehran and the Caspian Sea in the Alborz mountains.
A local emergency official said the bus was carrying 40 people, including 25 women and five children, and that all of the victims were Iraqis.
The injured were transported to hospital in the nearby town of Chalus, the official added.
The accident happened during heavy traffic as Iranians took to the roads ahead of a three-day national holiday.
Despite its road network being in good condition, Iran has a poor fatality record, with more than 18,000 people killed in 2014, according to official figures.
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