The Qatari went off-piste and hit a hole at around the 414 km mark. The winner of the first stage, and runner-up on day two, got going about an hour later at slow speed but had to stop again after another 30km.
While Al-Attiyah is likely to continue, with the rally heading to Bolivia and Paraguay before ending in Buenos Aires, the setback means he will have to focus on individual stage wins rather than the overall prize.
"Game over. A bad day," he told the Dakar website (www.dakar.com) after ending the day 32nd overall. "We hit the other side on a big stone and we broke the wheel completely.
"We decided to use some rocks and the wheel to make up the balance but we had to drive 80km like this. We stopped to repair but we could not. We don't have all the parts.
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"It was a mistake ... it's bad luck but this is the race. This is how the Dakar is. We were doing a really good job, we were leading but there you go..."
Wednesday's stage, reaching 5,000 metres in altitude, ended as a one-two-three for Peugeot.
Frenchman Loeb leads, 42 seconds clear of Spanish team mate and former world rally champion Carlos Sainz -- the father of the current Formula One driver of the same name -- with Peterhansel third after his first stage win of this year's event.
Peterhansel, who is chasing his 13th Dakar success after six titles in cars and six on motorbikes, is now four minutes and 18 seconds behind Loeb, who had started the day 28 seconds clear of Al-Attiyah.
(Reporting by Alan Baldwin in London, editing by Peter Rutherford)
