The blaze happened at the rear of Tesco in Wharf Road, Ellesmere, at around 11pm on Friday.
A Shropshire Fire and Rescue spokesman said: "At 11.04pm on Friday, September 23, SFRS Fire Control received a call reporting a car fire in Ellesmere.
"One fire appliance was mobilised from Ellesmere. Crews used a hose reel jet to tackle the fire.
"Also at the scene of the incident were the police."
West Mercia Police have been contacted for an update.