The automaker is contacting owners by telephone and by mail to tell them to refrain from driving the cars and to immediately contact their dealers.
Because of the potential fire risk, the company is also advising owners not to park their vehicles in or near any structures until they are repaired.
Mayne said the cars covered by the recall are powered by 3.6-liter Pentastar V-6 engines.
Chrysler said a single shipment of electrical components that are used with that specific engine arrived at the Ontario factory, where the car is built, with an improper configuration.
Workers at the Brampton factory in Ontario, Canada, attempted to fix the faulty components, but the repair used led to the potential fire hazard, causing the recall.
Chrysler discovered the problem when it noticed a pattern of reported incidents. The company said 50 of the affected cars are in customer hands in Canada, and 350 of the cars are in customer hands in the Middle East.
Chrysler said it will provide a free loaner vehicle until repairs are complete.
Challengers with V-8 engines are unaffected, as are all Dodge Chargers and Chrysler 300s, which are also built on the same assembly line in Brampton, Ontario.