Khuzestan, Kermanshah, Ilam and Kurdistan provinces were all affected, and state television cited local officials as blaming the closures on high levels of accumulated dust.
Government and private offices also shut in several provinces including Kermanshah and Ilam, as well as Khuzestan in the southwest.
Zanjan in the northeast and Bushehr in the south were also hit.
Bushehr, nearly 1,100 kilometres (680 miles) south of Tehran, was given an Air Quality Index of 108 on Tuesday, rated "poor for sensitive groups".
That figure is more than four times higher than the concentration of air microparticles deemed acceptable by the World Health Organization.
Iran's meteorological authorities said the conditions were caused by "the movement of a large mass of dust from Iraq towards western Iran".
State television reported low visibility in some areas and urged people to remain inside and wear face masks if they had to go out.
Last month, a similar dust storm in Iraq grounded flights and sent thousands of people to hospital with breathing problems.
On Monday, Iran's IRNA state news agency said more than 240 people in Khuzestan province had been treated for respiratory issues because of the dust.
A spokesperson for the emergency services also told Tasnim news agency on Tuesday that nine people had died as a result of storms in Iran over the past seven days, ending on Monday.
"Four of the deaths were caused by strong winds and falling objects, and five were caused by lightning strikes," it added.
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