A stop-delivery order has been issued to Chevrolet dealers until the cars are repaired.
"The left-rear or right-rear parking brake cable brackets may not have been properly fastened during the assembly process," said NHTSA in its recall summary. "As a result, the fastening bolts may back out completely, causing the parking brake bracket to separate and the parking brake to not hold the vehicle in place."
The problem increases "the risk of a vehicle rollaway and a crash," NHTSA added.
GM spokesman Alan Adler told Edmunds the automaker "knew of no crashes, injuries or fatalities related to this condition, which was discovered February 9 during a plant audit."
This is part of a larger recall of 2,062 Cruze cars in North America.
Chevrolet dealers will inspect for proper torque and, if necessary, tighten both the left and right rear park brake cable bracket bolts. The recall is expected to begin on March 24. Owners can contact Chevrolet customer service at 1-800-222-1020.
Edmunds says: Recall notices should go out shortly. If you have an immediate concern, contact your dealer now.