The problem is due to a possible malfunction of the hood safety system and hood lock system.
"If the hood unexpectedly opens while driving, it may interfere with the driver's visibility, increasing the risk of a crash," said NHTSA in its recall summary.
There are no injuries, crashes or fatalities linked to the recall, Subaru spokesman Michael McHale told Edmunds on Wednesday.
Subaru told federal safety regulators in a chronology of the recall that it received notification of a lawsuit concerning a 2006 Tribeca on September 30, 2015. The lawsuit claimed that the hood opened while the vehicle was being driven.
In October 2015, Subaru conducted an investigation in the U.S. on a vehicle with the same complaint, the company said.
The recall will be conducted in two phases, since final repair parts are not yet available.
In phase one, Subaru dealers will inspect, clean and lubricate the hood safety and hood lock systems. If the hood latch does not operate properly at this point, it will be replaced.
Phase two will involve installing an improved hood safety system and hood lock system.
A date has not been set for the recall, but Subaru said it planned to notify owners within 60 days.
Owners can contact Subaru customer service at 1-800-782-2783.
Edmunds says: Owners should be prepared to take their vehicle to the dealership twice for this repair. Those with an immediate concern should contact their dealer now.