The blaze broke out around 11pm last night at the car park on Albert Road, Meersbrook, with firefighters dispatched to the scene to deal with the blaze.
One shocked onlooker described a car having been set on fire. She said: “It just exploded. There are loads of cars.”
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A nearby resident later described hearing a crash, and then a shout, before the sound of a car door closing and a vehicle driving off.
She said an initially small fire appeared to spread along the side of the car.
She said one man later appeared to go towards the car, possibly to check there was no one inside, but having already seen it was empty, she shouted him to stay away as the fire service were on their way.
It is believed the car was a taxi.
South Yorkshire Police have this morning confirmed they are treating the fire as a suspected arson attack.
They said in a statement: “Emergency services were called at around 11.07pm last night (Tuesday July 5) following reports of a car on fire at Albert Road, Meersbrook.
“It is believed the fire was started deliberately. Three cars were damaged in the incident.
“Enquiries are ongoing. Anyone with any information should call police on 101 quoting incident number 1056 of July 5.”
South Yorkshire Fire and Rescue Service said in a statement: “Central firefighters were called out to an accidental car fire at 11.05pm on Albert Road, Heeley, Sheffield. The crew came away at 11.35pm.”