English-language Press TV said Cohen had been ill for several years and was buried on Sunday in Tehran.
Fars news agency said Cohen had been the spiritual leader of the Jewish community in Iran since 1994.
Mashallah Golestani Nejad took over the position after his death, said Press TV.
According to a 2011 census, some 8,750-20,000 Jews live in Iran, compared to 80,000-1000,000 before the 1979 Islamic revolution.
Jews -- who live mostly in Tehran, Isfahan and Shiraz -- are recognised as a religious minority along with Christians and Zoroastrians.
It operates schools, a library and a hospital -- which relies in part on public funds -- in Tehran.
The election of President Hassan Rouhani in June 2013, a reputed moderate, raised hopes among the community for an improvement of their standing. His hard-line predecessor, Mahmoud Ahmadinejad, gave regularly anti-Israeli tirades during his two terms in office.
Both Rouhani and Foreign Minister Mohammad Javad Zarif congratulated the Jewish community for their New Year in early September. They have also condemned the Holocaust.
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