The 46-year-old, the 2011 and 2015 champion, would not start Thursday's fourth stage after losing the wheel of his car during the previous day's special.
Al Attiyah came to a halt for over an hour when he damaged a wheel on his vehicle.
"The damage to his Toyota Hilux is too extensive to be repaired by his team," organisers added.
Al Attiyah had been among the pre-race favourites and was sitting second in the overall standings ahead of Wednesday's stage.
The fourth day of the Dakar Rally is 521km from San Salvador de Jujuy in Argentina to Tupiza in Bolivia with French driver Sebastien Loeb leading the race.