Price and Sunderland were early contenders for a podium but suffered an axle failure on Stage 4, losing five hours as they waited for help.
On Sunday, the Australian revealed his co-driver had suffered a concussion during the fateful stage and kept it hidden.
However, another hit to the head worsened Sunderland’s condition and the team elected to withdraw.
“Unfortunately we’ve chosen to withdraw from the Dakar Rally due to medical reasons,” said Price.
“Sammy suffered a concussion on Thursday which we kept on the down low because he really wanted to soldier on like the true fighter he is.
“Today we had an issue with the car that pushed us back into the dust with poor visibility and Sammy took another blow to the head, losing vision and making his concussion worse.
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“I feel it’s not fair to keep going because we have so much more to lose than gain.”
This year’s Dakar Rally was Price’s first on four wheels after a decade riding for KTM, winning in 2016 and 2019.
Price, who was competing for Overdrive Racing in a Toyota HiLux, expressed his disappointment at the early exit.
“It’s a shame to finish like this and we’re both gutted,” he said.
“We can fix cars but not humans, and Sam is family to me so his health comes first.
“We can’t thank everyone enough for their support, especially Black Rock Motor Resort and Overdrive Racing.
“It means the world to us and we wouldn’t be here without each and every partner that helped bring this to life.
“Hopefully this won’t be our last one, time will only tell and thank you all again, it’s been a wild ride.”
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