The stage will have no official winner, but the yellow jersey goes to Bernal as he crossed the summit first and was racing downhill with Simon Yates when the pair were told of the danger ahead, the road to Tignes buried in hail and rubble.
Bernal led atop the Col de l'Iseran in the Alps where the race times were taken when the stage was halted.
The 22-year-old will become the first Colombian to win the race should he hold on over the 33km climb on Saturday's summit finish in the Alps with just Sunday's procession into Paris to follow.
Bernal attacked on Friday's last climb, about 5km from the summit, with defending champion Geraint Thomas, plus title rival Steven Kruijswijk trailing around a minute behind.
Overnight leader Julian Alaphilippe was a further minute adrift and was disconsolate after the race.
"I don't think I can win the yellow jersey back," said Alaphilippe who is 45 seconds off the overall lead. "I was beaten by something stronger than me."
Alaphilippe wore the yellow jersey for 14 days, carrying the hopes of a public eager to see a French winner for the first time since Bernard Hinault in 1985 and defying pundits who felt he would wilt in the Pyrenees.
Bernal's family and girlfriend were waiting for him at the official presentation, where he strode towards the podium with calm dignity as many of his entourage cried openly.
"I was going at great speed when they told me to stop and I said no way, not now, please," he said.
"But they told me it was okay, I was the new leader, and then I accepted it and pulled over," said the youngest man on the race.
"We aren't in Paris yet. But I feel like crying. Tomorrow will be hard and I will do everything to defend this," he added.
Bernal attacked on Friday's last climb, about 5km from the summit, with defending champion Geraint Thomas, plus title rival Steven Kruijswijk trailing around a minute behind by the time the Colombian crested.
Many felt it was the right decision to call off the race.
"It was the only decision possible, imagine what might have happened?" FDJ sports director Marc Madiot said.
Ineos may feel robbed of a further opportunity because Bernal looked set to pulverise the overall standings.
Ineos led the ascent of the Col de l'Iseran with three men, Wout Poels, Dylan van Baarle and Jonathan Castroviejo ahead of Thomas and Bernal.
With the isolated Alaphilippe struggling for breath towards the summit of the highest point of the Tour, Bernal attacked 5km short of the peak, scampering away with ease.
Earlier, France's other yellow jersey hope Thibaut Pinot was also ruled ut.
Trailing behind the peloton in tears, Pinot pulled out an hour into the race, still suffering from the thigh injury picked up in a crash two days ago.
The FDJ contender for overall victory was fifth at the start of a stage which suited his qualities.
When he dismounted from his bike he ended a roller-coaster ride which included victory atop the first Pyrenean climb to the summit of La Col du Tourmalet, where his performance put him in the frame for a tilt at the title.
Saturday's 20th stage finishes with the longest climb of the Tour at the end of which the race leader will be the de facto winner, ahead of Sunday's parade through Paris and sprint finish on the Champs Elysees.