According to the California Highway Patrol, Hart was being driven in his 1970 Plymouth Barracuda on Mulholland Highway at the time of the accident.
His wife Eniko Parrish told TMZ news reporters on Monday that the comedian was awake and "going to be just fine".
The accident happened just after midnight.
The driver, Jared Black, lost control of the car and it tumbled into an embankment, the report stated.
Black also sustained major back injuries. A third passenger was unhurt.
Black - the fiance of the third passenger, Rebecca Broxterman - was determined not to have been driving under the influence at the time of the crash.
Hart was taken to Northridge Hospital Medical Centre and the driver was taken to another hospital, the patrol report said.
Hart is known for his stand-up comedy and comic roles in movies such as Ride Along and The Secret Life of Pets.
He pulled out of hosting this year's Oscars ceremony following a controversy over old homophobic tweets.
The 40 year old said he did not want to be a distraction and was "sorry he had hurt people".
The ceremony went ahead without a host.