May 26, 2017 0529 GMT
The electric car maker said about two percent of the 53,000 vehicles built from February to October 2016 were affected, but all of those cars are being recalled, BBC wrote.
The company added it had no reports of accidents or injuries relating to the brake issue.
In a statement the firm said the electric parking brakes installed on Model S and Model X "may contain a small gear that could have been manufactured improperly by our third-party supplier".
If the gear were to break, the parking brake would continue to keep the car from moving, but the parking brake would be stuck in place, it added.
Tesla said there had been no reports of parking brake failure, and said it was "safe to continue regular use of your vehicle."
The company will be sending an official recall notice to customers, with information on how the parking brakes could be replaced.
In 2013, the National Highway Traffic Safety Administration, a US federal government agency, awarded the Tesla Model S a 5-star safety rating, and said the vehicle "set a new record for the lowest likelihood of injury to occupants".
The company issued a voluntary recall for 3,000 of its Model S cars in November 2015, due to seatbelt connectivity problems.
Tesla produced a total of 83,922 vehicles in 2016, including the Model S and Model X.
Earlier this week chief executive Elon Musk said Tesla would unveil an electric articulated lorry in September. Additionally, he said an electric pick-up truck would be shown off in the next two years.
Last year Musk expressed the firm's desire to branch out beyond cars, but analysts are concerned the company will not meet demand for its current projects.
The Model 3, a more mid-market car compared with Tesla's current offerings, has 400,000 pre-orders which is vastly more than the company can manufacture in a year. It is due to go into production later this year.
Tesla faces competition from other similarly priced electric cars that will become available first, including General Motors' Chevy Bolt and BYD's Qin EV300.