Federal safety regulators said they are looking into "allegations of fire or smoke from the engine compartment" of the vehicles.
The single complaint alleges "a severe engine compartment fire incident resulting in a total vehicle loss," said NHTSA in its summary of the investigation. "The consumer alleges that the entire vehicle was engulfed in flames approximately 20 feet high within seconds of parking the vehicle.
"The complaint alleged white smoke coming from under the hood immediately after parking the vehicle and while the ignition is off."
Federal safety regulators said they have also "identified field report data submitted as part of Early Warning Reporting that relate to the alleged defect." No details were provided.
No injuries or fatalities are linked to the probe, according to NHTSA.
NHTSA has opened what is called a "preliminary evaluation" into the matter. Such an action sometimes precedes a vehicle recall, but the 2015 Cherokee has not been recalled at this point.
"We are aware of this incident and our investigators are cooperating fully with NHTSA's preliminary evaluation," wrote Fiat Chrysler Automobiles spokesman Eric Mayne in response to a query from Edmunds.
Edmunds says: Owners of the 2015 Jeep Cherokee will have to wait until federal investigators finish their work before taking any action. If you have any concerns about your vehicle now, it's best to contact your Jeep dealer.