The federal agency says the affected vehicles from model years 2007 to 2014 have a 220-amp alternator with a potential to malfunction in hot weather.
It says the problem can be corrected by replacing the alternator.
The recall affects Ram 2500 pickup trucks from the 2013 model year, 3500s from as early as the 2007 model year and Ram 4500 and 5500s from the 2008 through 2013 model years.
It also affects the Dodge Charger police cars from the 2011 through 2014 model years.
There are also recalls in the U.S. and Mexico.
In an Oct. 18 statement, Fiat Chrysler says it is aware of a possible injury in the U.S., but no collisions.
The automaker is recalling about 74,833 vehicles in the U.S., 1,088 in Mexico and 134 outside the NAFTA region.