The fault centres on the vanity lamp integrated into the sun visor, which could experience a high resistance short after a service repair or while accessing the space behind the headliner.
The company reports that the fault may lead to an inoperative vanity lamp, or worse, an electrical fire.
FCA Australia has confirmed that 11,345 Grand Cherokees are listed in the recall, with owners of affected vehicles to be contacted by mail. Concerned owners can contact FCA Australia on 1300 133 079.
The recall forms part of a wider action that has seen more than 600,000 Grand Cherokee and Dodge Durango models recalled in North America for the same issue.