The 2015-'16 Chevrolet Tahoe police vehicle is included in the recall.
"The brake pedal pivot nut on these vehicles may become loose, causing the brake pedal to be loose or inoperative," GM said in a statement.
There are no reports of accidents or injuries linked to the recall.
Chevrolet dealers and GMC dealers will inspect the pivot bolt installation to determine whether the vehicle has already received the production remedy. If not, the dealer will add adhesive to the nut and reinstall the nut at an increased torque.
GM spokesman Tom Wilkinson said customers will be notified of the recall shortly.
No information about the recall has been posted on the website of the National Highway Traffic Safety Administration, which oversees vehicle safety in the U.S.
Edmunds says: Owners of these vehicles should be ready to make a service appointment with their dealer soon.