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He was able to continue but his team later said he would be withdrawn from the race due to concussion.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.
Bardet pushed off with just under 7km remaining of the final ascent up the 14.7km Pico Villuercas climb.
Having been part of an 18-man breakaway, Bardet – of Team DSM – could not be caught and crossed the line 44 seconds ahead of Jesus Herrada, while Jay Vine came third despite crashing into his team car around midway through the stage.
Odd Christian Eiking kept hold of La Roja, though was unable to keep pace with Primoz Roglic, who edged ahead of Miguel Angel Lopez to gain 20 seconds on the race leader.
Enric Mas, Egan Bernal and Jack Haig managed to stay with two-time defending champion Roglic, who will be looking to make his prowess in the mountains count during a gruelling stage on Sunday.
"It's been a long wait. It means a lot. I've been second too many times," said Bardet, who has now taken the king of the mountains jersey, after claiming his first stage win at a Vuelta.
"Today I went full gas to be in the good break. I know that taking the polka-dot jersey it'd be a double victory. It's fantastic.
"I think we played it smart with my sports director and he told me exactly when to attack on the steepest part of the climb and go for it as if the finish was there in front of me.
"I opened a good gap and made it to the finish. Everyone is tired but the spirit is so high in the team, so the moral is high. We're all focused and I'm so happy to be part of a good group of guys.
"We're enjoying ourselves and trying to do our best for the team. It's an amazing Vuelta."
STAGE RESULT
1. Romain Bardet (Team DSM) 4:20:36
2. Jesus Herrada (Cofidis) +0:44
3. Jay Vine (Alpecin-Fenix) same time
CLASSIFICATION STANDINGS
General Classification
1. Odd Christian Eiking (Intermarche-Wanty-Gobert) 55:3:17
2. Guillaume Martin (Cofidis) +0:54
3. Primoz Roglic (Jumbo-Visma) +1:36
Points Classification
1. Fabio Jakobsen (Deceuninck-Quick-Step) 200
2. Magnus Cort Nielsen (EF Education–Nippo) 114
3. Primoz Roglic (Jumbo-Visma) 106
King of the Mountains
1. Romain Bardet (Team DSM) 50
2. Damiano Caruso (Bahrain Victorious) 31
3. Michael Storer (Team DSM) 17
What's next?
Four categorised climbs await the riders on Sunday, across a mammoth 197.5km route from Navalmoral de la Mata to El Barraco.
