Owners also are being told not to park the cars in a garage or near a structure until the problem can be fixed.
The cars are from the 2013 model year and have V-6 engines. They were made during an eight-week period that ended Jan. 24.
Chrysler wouldn't identify exactly where the short occurs, but said it's in a place that most owners would never see. Seven fires were reported that damaged cars, but no one was hurt, the company said in a statement.
The company is notifying owners by telephone and mail and will provide loaner cars until repairs are made, at no cost to the owners. Chrysler also will transport the cars to dealerships to make the repairs, spokesman Eric Mayne said.
Challenger owners who have questions should contact their dealers, he said.
The recall also affects another 1,900 cars on dealer lots that haven't been sold.
Mayne said a shipment of electrical components arrived at the company's Brampton, Ontario, assembly plant that weren't configured properly. Workers at the plant reworked the components, but the change caused the short circuits, he said.