The video showed plumes of smoke rose into the sky amid the sound of an alarm, but firefighters extinguished the flames within hours.
According to the report, the incident happened after a clash among a number of prisoners convicted of financial crimes and theft.
The prisoners reportedly set fire to a warehouse full of prison uniforms, which caused the blaze, but security forces intervened to restore calm.
IRNA reported that at least eight people were injured in the incident, but there are no reports of deaths.
