The Volvo bus, carrying 44 passengers, was travelling on the key artery from the southeastern province of Kerman towards Tehran at 7:40 AM when the driver fell asleep, local officials told ISNA.
The driver was among those killed.
Iran is one of the deadliest countries in the world for road accidents, according to the World Health Organisation.
In December, a bus carrying students along a mountainous road in northwestern Tehran veered off the road and hit a concrete column, killing 10.
Efforts to modernise Iran's ageing and highly polluting vehicle fleet have been hampered by a lack of investment.
Auto giants Peugeot and Renault have been forced to suspend plans to open new factories in the country due to the return of US sanctions.
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