Reza Dehghanpour told the Tasnim News Agency that one individual died when a tree broke off and fell on top of him and three others lost their lives as they were hit by falling debris.
He added that the dust storm also left 15 people injured in the capital city.
Dehghanpour said the level of damage caused by the record winds is still uncertain.
Monday’s storm roared into the capital with winds of up to 110 kilometers per hour.
It caused temporary power outages in some districts of Tehran and broke trees. It also caused a chain-reaction crash on a highway south of the capital with 20 vehicles and caused international flights to be cancelled.
