The Etixx-QuickStep rider fell inside the last kilometre of the 191.5km stage from Abbeville to Le Havre while wearing the yellow jersey for the first time in his career, an honour he won by claiming victory on Stage 4.
Martin suffered a compound fracture of the bone, which pierced his skin as well, and was flown on Thursday night to Hamburg to go under the knife.
“The surgery went well. Martin will have to respect a period of rest of two weeks before resuming training,” a team statement read.
Had he been able to continue in the Tour, Martin would have been able to see his remaining team-mates help Mark Cavendish cross the line first on Stage 7. A calculated sprint finish saw the Briton claim his first stage victory at the Tour de France since 2013.
“I would like to thank all the people involved in my transportation to the hospital and the medical staff in Hamburg” Martin said.
“They were all amazing and they allowed me to undergo surgery in such a short time after the crash. In these situations, time is an important factor and we couldn’t have done better.
“I wish good luck to my team and to all the riders busy at the Tour. I will follow the race on TV today from the hospital. It will be strange, but that’s life and cycling.”
The 30-year-old German, a three-time UCI world time trial champion, remains positive after what can only be described as a rollercoaster first week at the Tour.
“I have to try to see the glass half full and keep the good memories,” he said.
“I had a great first part of the Tour with a great team around me. I won a stage and wore the yellow jersey for the first time in my career. A dream came true during this Tour and now I’m already looking forward to coming back one day again and living the great emotions of this race.”
Martin’s crash did not affect his position in the general classification ahead of Stage 7. He was 12 seconds ahead of Chris Froome (Sky), but the German was unable to start the stage as a result of his injury.
However Froome, the 2013 Tour de France champion, elected not to wear the iconic garment out of respect for his fellow professional, so the stage went ahead without anyone in the maillot jaune.
Froome did, though, take the jersey at the end of the stage, and the Team Sky leader will start Stage 8 with it on his back.