The Etixx Quick-Step rider went down inside the final kilometre of the sixth stage on Thursday after touching wheels with the rider in front of him.
"I was unlucky. I don't even remember how I went down. I touched the rear wheel of the rider in front of me – Bryan Coquard – but it's the Tour, luck and bad luck are always close," he told BBC Sport.
Zdenek Stybar, Martin’s team mate, was able to avoid the crash and cruise to stage victory. Martin was able to finish the stage with the assistance of his team mates, but held his left arm to his body the entire way and was clearly in pain.
Great Britain’s Chris Froome, of Team Sky, trailed the German by 12 seconds on the general classification but will now move into the lead.
Martin is the second leader to crash out of Le Tour already. On Monday Fabian Cancellara was forced to withdraw after fracturing two vertebrae in his spine.