The fall happened with around 90km of the tough climbing stage left to race when riders near the front of the bunch fell on a gentle left hand turn on the road to Puy Mary.
It soon became clear that AG2R La Mondiale leader Bardet and Quintana (Arkea-Samsic), fourth and fifth on general classification, were involved in fall.
Trek-Segafredo’s Mollema was also involved in the crash, with reports suggesting he had pain in his right arm and shoulder and had a bloodied face.
The fall resulted in Mollema abandoning the 2020 Tour, forcing him to give up his 13th place on general classification.
Aerial footage of the crash shows a number of riders falling on the turn and riding into a ditch at the side of the road.
Both Bardet and Quintana were quickly able to jump back on their bikes and were paced back into the peloton by their team-mates, but it’s not currently clear if they suffered any injuries.
Trek-Segafredo said on Twitter: “Unfortunately Bauke Mollema was caught up in the last crash.
“He has abandoned and we will report the extent of his injuries when we know more.”
Mollema had been riding in support of his team leader Richie Porte but had still been riding well overall himself, sitting 2-31 off the race lead on the start of stage 13 and around 50 seconds away from the top-10.
The Dutchman has been a Grand Tour contender himself in the past, finishing third in the 2011 Vuelta a España. He also has three top-10 finishes in the Tour de France, including a sixth-place finish in 2013.