The 29-year-old Frenchman, riding for the AG2R La Mondiale team, was one of several riders involved in a nasty incident near the midway point of the 191.5-kilometre stage.
He was able to continue but his team later said he would be withdrawn from the race due to concussion.
Bardet sat fourth in the general classification before Friday's stage, just 30 seconds behind leader Primoz Roglic, and said the end to his race was "quite the opposite of what I expected".
He drifted to 11th in the standings by the end of the stage and accepted his fate when the team pulled him out.
"The crash was severe, downhill at high speed, and I struggled all the rest of the day," Bardet said.
"The medical examinations confirmed what I already suspected, and I am not able to continue in the race.
"I know that my team-mates will give their best to finish the Tour de France with strong performances."
A team statement said: "Romain is suffering from a concussion the intensity of which he showed signs at the end of the stage, which necessitated that our medical team insist he undergo a brain scan at the Clermont Ferrand University Hospital, with the help of Dr Mathieu Abott of AS Montferrand.
"The CET scan did not reveal any lesions. However, Romain Bardet must stop all his sporting activities for the moment, and he will therefore not be able to take part in the start of the stage tomorrow."
Bardet has achieved five top-10 general classification finishes in his Tour de France career, going closest to overall victory when he was runner-up to Chris Froome in the 2016 race.
Peters made a major breakthrough with a maiden grand tour stage win on last year's Giro d'Italia, as well as finishing third in a Tokyo 2020 Olympic Games test event.
The 26-year-old rides for the AG2R La Mondiale team and says his last test stemming from the World Anti-Doping Agency's (WADA) ADAMS whereabouts system took place on October 7 last year.
He reported having a cortisolemia check carried out by the Movement for Credible Cycling (MPCC) union in March at the Paris-Nice race, but pointed out only certain teams belong and submit to testing by that body.
Like most sports, professional cycling has shut down during the COVID-19 crisis, with the Tour de France shunted back by two months to an August 29 start.
"What does it mean? Two options," wrote Peters on his personal website, considering the few doping checks he has been required to take.
"Either I have a profile that is not at all suspicious, which means I'm rarely tested, this is in effect the case since starting as a professional, where I was only checked three to four times a year.
"Or, and I'm very afraid of this, in this period of confinement there is no control!!!!!
"Let's not be naive, there is still doping, fortunately much less than in the years 1995 - 2005, but there will always be!
"Are cheaters free at the moment? It is as if we were told, 'Do you want to cheat? Well go for it! It's time, do what you want, take what you want, train like crazy at home now, you have until May 11 to get your engine going and crush everything when you return to competition'."
The Cycling Anti-Doping Foundation, which carries out testing in professional cycling, said in March it intended to be "continuing activities to protect clean cycling".
It said it would be following advice of WADA, which has said testing during the coronavirus period "will continue only where appropriate and possible".
Peters added: "I'm afraid for my sport, for my passion and for my end of the season facing mules!"
