The comedian and actor, 40, was reportedly being driven in his 1970 Plymouth Barracuda shortly after midnight on Sunday on Mulholland Highway when the driver lost control.
The car tumbled down an embankment, according to California Highway Patrol.
TMZ reported that Hart injured his back.
The driver, Jared Black, is also said to have suffered major injuries in the accident. He was not under the influence of alcohol at the time, CHP added.
Authorities said Hart, who is known for his stand-up comedy and comic roles in movies including Ride Along, was able to leave the scene of the crash with a second passenger, who was not badly hurt, and head to his home nearby to get medical attention.
He was taken to Northridge Hospital Medical Centre and the driver was taken to another hospital.
His publicist did not respond to requests for comment.