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The Australian, who was running second in the overall Bikes standings, crashed at the 155-kilometre point of Tuesday's ninth stage.
According to Dakar officials he is now being transported to hospital in Tabuk for further assessment of head, right wrist and left shoulder injuries.
The extent of those injuries is currently unknown, however organisers have confirmed he was conscious throughout on-the-scene treatment.
Price started the day sitting second in the bikes class, and had made progress on leader Jose Ignacio Cornejo (Honda) early in the stage.
He was third-fastest through the last waypoint before his crash.
Cornejo's Honda teammate Ricky Brabec, who had been fastest through that 121-kilometre reference, lost 15 minutes after stopping to assist Price, while the two-time event winner's fellow KTM rider Sam Sunderland dropped 14 minutes for the same reason.
Both will likely be awarded back time by the organisers at the end of the stage.
Later in the same stage, Luciano Benavides (Husqvarna) also crashed out, injuring his shoulder, and was also airlifted to hospital in Tabuk.
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Dakar 2021, Stage 9: Cornejo lead grows after Price exit