The flag carrier will operate roundtrip flights between the Iranian and Spanish capitals on Wednesdays.
The flights will depart from Imam Khomeini International Airport at 09:50 a.m. and the return flight will leave Madrid on the same day at 15:30 local time.
Based on a statement by Iran Air, passengers with Visa C (tourist visa) will not be allowed to take the flight till further notice.
The country has been trying to resume its international flights after the coronavirus pandemic hit the sector since early 2020.
The airline currently operates flights to Vienna, Amsterdam, Paris, Milan, Manchester and London.
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