Crews were called to the market town's High Street just before 14:30 GMT.
A number of people have been evacuated from nearby properties amid concerns the car could be fuelled by Liquid Petroleum Gas (LPG).
A fire service spokeswoman said: "We don't get many vehicle fires involving LPG but but it is explosive so we do take precautions."
Firefighters have been tackling a car blaze in the centre of Skipton.