The decision by the National Highway Traffic Safety Administration included 2016 models of SUV X and 2020 models of SUV Y.
This will be the largest Model X recall for Tesla at 9,136 vehicles. The SUV may have a faulty roof trim that could detach from the car and fly putting other bikes and cars on the road at risk.
Tesla said it first learnt of the issue in September last year.
The other recall covers 401 Tesla Model Y vehicles with bolts connecting the front upper control arm and steering knuckle that may not have been properly tightened.
Tesla said vehicles would be inspected for proper torque and if necessary, would be adjusted, Reuters reported.
Shares of the Palo Alto, Calif., company at last check were down 1.35% to $562.90.
On Tuesday shares of Tesla reached a market valuation of $500 billion for the first time.
Tesla's share price has surged in the recent past, driven by its approaching inclusion in the S&P 500 index. Tesla will join the index on Dec. 21.
Musk has been one of the biggest beneficiaries of the stock's rise. Musk's net worth jumped $7.2 billion on Monday, giving him an estimated worth of $127.9 billion.
Tesla received an upgrade from Wedbush Securities’ Daniel Ives, who lifted his one-year price target to $560 from $500 and said his new bull case is $1,000, up from $800.