Local media is reporting that 15 of the plane's crew were killed when the plane hit the ground and burst into flames.
The plane crashed at Fath Airport when it was meant to land at the nearby Payam International Airport, about 25 miles west of Tehran, the Iranian capital.
Iran's air force said in a statement that the fate of the crew, including their possible "martyrdom", was under investigation.
The plane's engines and wheels are spread across the crash site and images from inside the plane's hull show it is completely charred.
Pirhossein Koulivand, the head of the country's emergency medical services, said of the 16 people on board the plane, only the flight engineer was known to have survived.
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"The plane was a cargo Boeing 707 that overshot the runway during its landing", Iran's aviation organisation spokesman Reza Jafarzadeh told state broadcaster IRIB.
The plane took off from Bishkek, Kyrgyzstan, and was to have headed to the Payam airport, also located outside the capital.
It is not clear who owned the plane.
The report says the crash occurred as the plane was making a landing approach heading for the wrong airport and trying to land at a non-commercial airport near a residential area instead of a cargo airport some 2.5 miles away. The air force does operate Boeing 707s.