Some buildings have been damaged.
The Fars news agency said 16 people were on board and one survivor has so far been found.
The plane took off from Bishkek, Kyrgyzstan, and was to have headed to the Payam airport, also located outside the capital.
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It was not immediately clear who owned the plane.
Fath airport is in Alborz province, just east of Tehran.
Iran's air force said in a statement that the fate of the crew, including their possible "martyrdom", was under investigation.
State broadcaster IRIB showed footage of burning wreckage.
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The plane - which was carrying meat - had set off from Bishkek, the capital of Kyrgyzstan, and was heading for the worldwide commercial airport in Payam, west of Tehran. "It exited the runway during the landing and caught fire after hitting the wall at the end of the runway", the army.
Emergency crews work at the site of the plane crash on Monday.
A cargo plane has crashed near Payam International Airport in Iran.
In January 2011, when an Iran Air Boeing 727 broke to pieces on impact while trying an emergency landing in a snowstorm in northwestern Iran, killing at least 77 people.
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A total of 15 of the 16 people on board the ill-fated jet died in the crash, the Iranian military said in a statement.