Fire crews were called to reports of a car on fire at the car park near to the Immaculate Heart of Mary Roman Catholic Church and Primary School, off Harrogate Road in Moortown.
The incident happened at 3.15pm yesterday.
The fire was reported to have been started by an electrical fault in the car of a parent who had come to collect their child at the end of the school day.
Nobody was hurt as a result of the blaze.
When firefighters from Killingbeck and Leeds arrived three cars were well alight – a Vauxhall Zafira, a Renault Clio and a Ford Fiesta.
A fourth car, a Renault Scenic, was slightly damaged by fire.
Pupils were kept inside the school until the fire crews had dealt with the incident.