The vehicles will have safety monitors and may not operate in bad weather, making them more restricted than the fully autonomous vehicles promised by Elon Musk.
Mr. Musk says the driverless taxis could begin ferrying passengers on Sunday in Austin, Texas, where other companies already have similar cars on the road.
The limited regulatory approval is an early step toward Elon Musk’s goal of offering a Tesla self-driving taxi service.
The electric car company said profits climbed 17 percent in the third quarter as strong sales of energy products helped to make up for relatively slow auto sales.
Alcon Entertainment, the Hollywood company behind “Blade Runner 2049,” said it had denied a request to use images from the movie but that Mr. Musk did so anyway.
The company’s C.E.O. said the new autonomous vehicle, which does not have a steering wheel, would cost less than $30,000, but the technology still faces hurdles.
Elon Musk has said that the vehicle will add trillions to Tesla’s stock market value and that those who don’t believe him should sell their shares.
The General Motors subsidiary reached a settlement with the main auto safety regulator after one of its self-driving taxis struck a pedestrian in San Francisco last year.
Tesla says self-driving taxis will power its growth, but the company hasn’t said when such a service would be ready or how much it would increase profits.
The company led by Elon Musk is selling fewer electric cars, and its big bets on driverless taxis and artificial intelligence could take many years to pay off.