The member of the council which advises the Iranian leader is the first top official to die from the illness that has affected members of the country's leadership.
The state broadcaster said Mohammad Mirmohammadi, 71, had died at a hospital in Tehran.
Iran has the highest coronavirus death toll in the world after China, with 978 confirmed cases and 54 deaths.
The senior official's death comes as the number of people around the world who have died from coronavirus reached more than 3,000 on Sunday night.
One of the biggest outbreaks outside mainland China is in South Korea, where there are now more than 4,200 cases.
https://news.sky.com/story/covid-19-global-coronavirus-deaths-top-3-000-as-asian-stock-markets-plunge-11947682