Speaking at a Sunday meeting of the National Headquarters for Fighting Coronavirus, Rouhani said it has been decided that mosques in 132 cities be reopened on Monday.
He stressed that health protocols should be observed in the places of worship.
Friday prayers will also be held again in those cities, the president added.
Iran closed mosques and other religious sites in March to stem the spread of the coronavirus.
Classified a pandemic by the World Health Organization, the new virus, a respiratory disease known as COVID-19, emerged in the central Chinese city of Wuhan in Hubei Province late last year.
It has infected nearly 2.5 million people and killed more than 244,000 globally.
According to Iran’s Health Ministry, the number of people who have died from the coronavirus in the country was 6,156 and the total number of confirmed cases 96,448 as of Saturday.
More than 77,000 patients in Iran have recovered from the disease so far.