The Tehran-bound flight operated by the private carrier Air Memphis took off from Cairo airport, sources at the airport said.
Last month, Egypt's Tourism Minister Hesham Zaazou signed an agreement on operating non-stop flights between the two countries during a visit to Iran.
In February, Mahmoud Ahmadinejad became the first Iranian president to travel to Egypt since Iran's 1979 revolution ruptured diplomatic ties between the two most populous countries in the Middle East.
Tehran broke off relations with Cairo in 1980, a year after both Iran's revolution and Egypt's peace agreement with Israel.
The ties between Egypt and Iran have improved since the fall of Egypt's former autocratic leader Hosni Mubarak in February 2011. But the countries remain at odds over many regional issues, including Iran's continued support for embattled Syrian President Bashar Assad.
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