Mick Schumacher was ruled out of Sunday's Saudi Formula One Grand Prix after crashing heavily in qualifying and being flown to hospital in Jeddah for precautionary checks.
The 23-year-old German's Haas team said he would not participate in the season's second race despite being physically unhurt.
"There is a possibility that he'll have to stay for observation overnight at the hospital. Based on these facts and where we are, we have decided not to field his car tomorrow," team boss Guenther Steiner told reporters.
The next round is in Melbourne, Australia, in two weeks' time.
On Saturday, Schumacher was taken by ambulance to the circuit medical centre after being extracted from the shattered car, which split in two when lifted on to a recovery truck, and then flown by helicopter to the King Fahad Armed Forces hospital.
"He has no injuries which you can see, they just wanted to check on him and do some scans to see that there is no damage from the impact," Steiner told Sky Sports television.
He said Schumacher, son of seven-time world champion Michael, had spoken to his mother, Corinna.
Commentators estimated the car was travelling at 170mph (274kph) at the time of impact into the concrete barriers at the exit to turn 10, scattering debris across the asphalt.
The floodlit Corniche street circuit is one of the fastest tracks on the calendar.
It looked from television replays that Schumacher, who had been ninth fastest, lost control of the car on the kerbs, spinning and slamming sideways into the wall.
"Maybe he just tried a little bit too hard," said Steiner. "Here if you make an error there's no run-off. It's walls."
The crash was the second of the session, with Williams's Canadian driver Nicholas Latifi bringing out red flags in the first phase.
Steiner said the car would have had to be completely rebuilt, and parts from the crashed one would have to be sent back to the factory for checks.
Denmark's Kevin Magnussen will be the sole Haas driver in Sunday's race.