The Boeing 707 plane operated by Saha Airlines, which belongs to the Iranian military, had 157 passengers and crew members on board, state television reported.
A child died after trying to escape the flames by throwing himself in a river at the edge of the runway, IRNA said.
Iran’s official news agency said both passengers and crew members were forced to jump from the aircraft to safety, as the emergency slides did not work.
Several passengers had broken limbs and were taken to hospital, IRNA reported.
An airline official told state television that the landing gear fell into a hole at the end of the runway, causing the fire, but a civil aviation official said he could not say why the plane had caught fire.
Passengers criticised the design of the airport which allowed a river near the runway.
“I would like to know what a river is doing in an airport,” said one passenger interviewed by state television.
“Right from the take-off, the plane had problems. After the fire, people rushed to the exit and I saw a child fall in the river,” said another passenger whose name was not given.
Most of Iran’s commercial fleet was acquired by the country before the 1979 Islamic revolution, and the country has since been hit by US sanctions that have prevented it from buying new spare parts.
Most parts are bought second hand or on the black market.
