Officials say the crash happened due to a technical glitch during a training mission on Monday.
The warplane, an F-5, hit the ground near a school in Tabriz which was empty due to the Covid-19 pandemic.
The civilian who got killed was sitting inside the vehicle at the time of the incident.
An army officer identified the pilots as Sadegh Falahi and Alireza Hanifehzad.
He also praised them for sacrificing themselves as they managed to land the plane in an open area.