Under certain conditions -- such as a driver keeping his foot pressed on the brake while idling in park -- the brake transmission shift interlock, or BTSI, may malfunction, allowing what the automaker called "inadvertent movement" if the parking brake is not engaged.
While customers wait to have their cars repaired, the company's safety compliance chief urged drivers to deploy the parking brake.
The recall covers certain heavy- and light-duty Rams dating back to 2009. Drivers can check to see whether their vehicles are affected at safercar.gov.
Fiat Chrysler said it was aware of seven possible injuries and "a small number" of accidents related to the glitch.