Priestley, best-known for starring in US teen soap Beverly Hills 90210, suffered a fractured spine, concussion, a head injury, two fractured feet and a broken nose during the accident on Sunday.
A doctor at the University of Kentucky Medical Center in Lexington, US, said the actor could recognise family and friends, and there were no signs of paralysis.
"I don't think the spine fracture is significantly more worrisome than the other injuries," Dr Andrew C Bernard said on Monday.
"His concussion is equally concerning to me. He has not yet recovered from the concussion enough for us fully to evaluate it."
The actor, who competes on the Indy competition's Infiniti Pro Series circuit, was helped by the fact that he was physically fit, Dr Bernard said.
"He has a number of injuries, each requires its own period of time for recovery. It would certainly be weeks before he'd be back doing most of the things that he likes to do."
Priestley is not being sedated and his foot injuries will limit his mobility, Dr Bernard added.
The actor had been due to compete in a race at Kentucky Speedway, having come second in the qualifying round on Saturday.
Former Indy 500 winner Arie Luyendyk saw the crash from the roof of the press box and said the actor hit the wall head-on.
"He got sideways and he corrected and then shot off the track," said Mr Luyendyk, whose son Arie Jr competes with Priestley.
"He turned right into the wall, and his first impact was basically head-on.
"What I'm thinking is, that's really the one big hit that he took that might have hurt him."
Mr Luyendyk added that Priestley appeared to have driven through some "oil-dry", an absorbent material that was spread on part of the track 10 minutes earlier to soak up an oil leak from another car.
Stage actor
Indy Racing League vice-president Fred Nation said that the drivers had been warned not to go through the substance.
Priestly became a worldwide star and heartthrob when he played Brandon Walsh in Beverley Hills 90210 between 1990 and 1998.
But he is not just known for his TV role - he branched out in 2000 at London's Apollo Theatre in a critically acclaimed production of the hit Broadway play Side Man.
It marked his West End debut and his return to the stage following a 10-year absence.
Prison
His film credits include Love and Death on Long Island, Tombstone and Eye of the Beholder.
Last year he finished an alcohol treatment programme imposed after a drink-drive conviction in 2000.
Priestley, from Vancouver, Canada, crashed his silver Porsche into a lamp post, a parked car and some dustbins in the Hollywood Hills in December 1999.
The incident destroyed the car, while his passenger and best friend Chad Cook suffered a broken arm.
Priestley was sentenced to five days in prison by Los Angeles Superior Court Judge Michael Pastor last year.
Judge Pastor also ordered Priestley to serve three years probation and enter a drug and alcohol treatment programme.
The actor's driving licence was suspended for a year.