Abdi had recently been hospitalized following a heart attack. He died on Friday despite medical treatment, Press TV reported.
Born in Tehran in 1960, Abdi began his screen career in the early 1980s with television productions before rising to national fame through the popular children's series I'm Late for School Again.
He made his film debut in The Great Controversy and quickly established himself as one of Iran's leading comic actors with performances in films such as The Man Who Became a Mouse, The Tenants, and Grand Cinema.
He won his first Crystal Simorgh, Iran's top film award, for his portrayal of Gholamreza in Ali Hatami's acclaimed drama Mother. More than two decades later, he earned a second Crystal Simorgh for Reza Attaran's comedy I Feel Sleepy.
Among his most enduring performances were in The Snowman and Mohsen Makhmalbaf's Once Upon a Time, Cinema.
Over a career spanning four decades, Abdi appeared in more than 120 films and television productions, becoming one of the most recognizable figures in Iranian cinema.
MNA