The Belgian infiltrated the day's breakaway and was sprinting for ninth place on the day when a touch of wheels brought him down, according to a statement from his team.
"A touch of wheels in front of our climber left him with nowhere to go but crash into the Mitchelton-Scott rider in front of him," the team said in their statement. "While Pauwels could still finish the stage, unfortunately the damage was severe as he suffered a broken elbow as a result of the crash and is now out of the Tour de France."
Team doctor Jarrad Van Zuydum said the injury will require surgery.
"He has come down quite hard on his right elbow and fractured the olecranon process of the right elbow," Van Zuydum said. "It’s actually an injury he has had on the left side before, and it is something that requires surgery to fix. We are already making arrangements for him to have surgery in Antwerp, and he will be back on the trainer pretty soon after that surgery, but obviously we are all very disappointed about the crash."
Pauwels, 34, finished the stage in 22nd place and was 28th overall, more than half an hour behind current race leader Geraint Thomas (Team Sky). Pauwels was also third in the mountains classification, three points behind Warren Barguil (Fortuneo-Samsic) and 26 points behind leader Julian Alaphilippe (Quick-Step Floors).
With his departure, Dimension Data are now down to just five riders after Mark Cavendish and Mark Renshaw missed the time cut on stage 11.