The affected Mustangs are equipped with a 2.3-liter engine.
"Prolonged exposure to elevated underbody temperatures might cause degradation of the fuel tank and fuel vapor lines, which could eventually result in a fuel leak," Ford said in a statement. "In addition, prolonged exposure to elevated underbody temperatures might cause the parking brake cable seals to degrade, potentially affecting parking brake functions.
"A fuel leak in the presence of an ignition source increases the risk of a fire. Impaired parking brake function could result in unexpected vehicle movement, which might increase the risk of injury."
Ford said it is not aware of any accidents, injuries or fires linked to the recall.
The affected Mustangs were built from February 14, 2014 to February 10, 2015 at Flat Rock Assembly Plant.
Ford spokeswoman Kelli Felker told Edmunds the recall will begin on July 6.
Ford dealers will replace the current fuel tank shield with a shield with a better-insulated shield, as well as install thermal patches on the fuel tank and parking brake cable and thermal wraps on the fuel vapor line.
No information about the recall has been posted on the Web site of the National Highway Traffic Safety Administration, which oversees vehicle recalls in the U.S.
Owners can contact Ford customer service at 1-800-392-3673.
Edmunds says: It will take several weeks for this recall to begin. If you own one of these cars and have an immediate concern, it's best to contact your dealer now.