The incident occurred with 60km remaining on Friday's stage to Carcassone, with several riders coming off on a downhill road that was lined by a gravelled surface.
Simon Yates (Team BikeExchange) and Roger Kluge (Lotto Soudal) abandoned at the time, but the crash has now forced two more exits.
Kragh Andersen was one of a number of DSM riders who fell down the ravine at the roadside and had to scramble out. The Dane rode most of the remaining 60km alone and finished second last, 16 minutes down on the peloton.
After the stage, he was placed under overnight observation by his team's medical staff and was diagnosed with a concussion.
“We closely monitored Søren during the evening and very quickly came to the decision that he was no longer fit to race after seeing some signs of concussion," said team physician Camiel Aldershof.
"Søren will now take a complete period of rest and we will continue assessing his progress, before we consider a plan for his return to the bike."
After winning two stages at last year's Tour, it's a sorry end to a tougher outing this time for the 26-year-old. He was caught up in crashes earlier in the race and was already suffering in the second week, fighting to finish just three seconds inside the time limit on the Mont Ventoux stage.
It's also a tougher Tour for DSM in general, who won three stages last year but have yet to make an impact, with Kragh Andersen becoming their third rider to leave as a result of crashes following Jasha Sutterlin and Tiesj Benoot.
"I am really disappointed and don’t want to leave the Tour de France. In my heart I know that the decision of the team’s medical staff can only be right one," Kragh Andersen said.
"I hope this is the last of the bad luck for the guys here at the race, and I wish them all the best for the final week.”
The other non-started on stage 14 was Barguil, who has also hit the deck several times so far and who was caught up in the same crash on Friday.
The Frenchman finished in a group four minutes down on the peloton but was suffering and announced his withdrawal on Saturday morning.
"Unfortunately I won't be at the start of stage 14, which had been an objective of mine since the parcours suits me well. Yesterday I came down in the big crash on the gravel descent. I was able to finish the stage and I wanted to finish the Tour, but I think it was one crash too many.
"My back and backside were affected, which has made it difficult to put power through my right leg. Along with the team and medical staff, we decided it was better not to start.
"It's heartbreaking for me. I've been through many emotions on this Tour and on the Tour in general. I'm not someone who normally abandons like this, but for health reasons it's important sometimes to know to say 'stop'."
Arkéa-Samsic's sprinter Nacer Bouhanni was also caught up in the crash but continues in the race, although the team are down to four riders after already losing Clement Russo, Anthony Delaplace, and Dan McLay.
Deputy Editor - Europe. Patrick joined Cyclingnews after a work experience stint in 2015 and hasn't left. Prior to that, he studied French and Spanish at university and went on to train as a journalist. Rides his bike to work but more comfortable on a football pitch.
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