Organisers hoped to start the stage at 1300 GMT after ferrying the riders to Monnetier-les-Bains by car.
``We did not want to endanger the riders' safety,'' said Jean-Marie Leblanc, president of the Tour de France. ``We took the decision with the team manager and all the race officials.''
The decision came as a relief for some exhausted favourites such as Spaniard Miguel Indurain and world number one Laurent Jalabert of France who lost their grip on the race at the weekend.
Powerful Russian Evgeny Berzin took the yellow jersey on Saturday after a stage finishing in the ski resort of Les Arcs.
The Russian, a former Giro d'Italia winner, gave further proof of his ability by crushing all his opponents' hopes in the individual time-trial on Sunday.
Berzin had been eager to tackle the two big climbs which had been scheduled for Monday -- the col de l'Iseran, which at 2,770 metres would have been the highest point of the Tour, and the col du Galibier (2,640 metres).
But the bad weather forced the organisers to cut out the two climbs.
``We had to skip l'Iseran because of heavy snowfalls,'' Leblanc said.
``We hoped to start from the other side of the climb but it appeared that le Galibier was far too dangerous too because of high winds blowing at about 100 kph,'' he said.
Winter conditions in the French Alps, with snowfalls and violent winds, reduced the day's ninth stage from a potentially gruelling 189.5-km ride from Val d'Isere to a short uphill course to Sestriere.
Organisers eventually decided to start the stage from a small village 46 kilometres from the Italian resort and the riders left Val d'Isere in team cars behind a snow-plough.
Riis, who started the stage second overall 35 seconds behind leader Evgeny Berzin of Russia, felt frustrated as all he saw of the Iseran and Galibier passes was from the window of a car.
``I thought this could be my day but when I saw what it was like when we drove by I understood it would have been impossible to have a race there,'' he said.
The veteran Dane, third in last year's Tour, attacked straightaway and reached the summit of the Montgenevre Pass near the Italian border narrowly ahead of a bunch composed mainly of the race favourites.
The powerful Riis, still going strong at 32, kept riding in front in the final punishing climb to Sestriere as Berzin gradually lost ground.
Frenchman Luc Leblanc, winner of a strenuous ride in the Alps on Saturday, and his compatriot Richard Virenque, eager to defend his ``king of the mountains'' jersey, came out of the chasing group in the last kilometres to take second and third places, 24 and 26 seconds behind Riis respectively.
Berzin had to be content with 14th place, one minute 23 seconds back, and lost the yellow jersey he had become the first Russian to wear after Saturday's stage.
Berzin is 40 seconds behind Riis in the overall standings. Swiss rider Tony Rominger, third in Monday's stage, is third overall, 53 seconds behind the leader.
Spain's Miguel Indurain, who had a rare off-day on Saturday when he lost over four minutes, seemed to have recovered as he led the pursuing group in the final climb to end the stage fourth.
``I felt better,'' said the five-times Tour winner who is a modest eighth overall, four minutes 38 seconds behind the new leader.
``Riis is very dangerous,'' added Indurain, bidding for a record sixth Tour win. ``I know I have to attack but I will not do it just anyhow.''
Spectators lining the roads in the Iseran Pass, who had been waiting for hours in the cold for the race to go by, behaved aggressively, shouting insults at race officials.
``What we did was dictated by common sense and by our concern for the safety of the riders,'' Tour director Jean-Marie Leblanc said.
``The conditions were against racing but it is the same for all of us and we have to cope with it,'' Virenque said.
The riders, exhausted by 10 days of awful weather, are looking forward to Tuesday's relatively undemanding 208.5-km 10th stage from Turin to Gap, which promises to be fairly dry.
Then, on Wednesday, they will enjoy a well-deserved rest day.
The Dane also took the overall leader's yellow jersey -- putting him 40 seconds in front of former tour leader Yevgeny Berzin and 53 seconds ahead of Switzerland's Tony Rominger.
It is the second time that the 32-year-old has claimed the yellow jersey -- he wore it in the 1995 Tour, where he ultimately finished third.
Riis, enjoying his third ever Tour stage victory after Chalons sur Marne in 1993 and Albi in 1994, attacked on the first climb to Montgenevre, and although he was reeled in by Berzin, a former teammate, and Abraham Olano, the Spanish World road race champion, he escaped again and was never to be caught.
"It's a magnificent day for me and the team. I was a little sad that we could not climb the first two mountains but when I drove over them I was happy that the right decision had been taken," Riis said.
"I decided to attack from the start and it was a case of now or never," he added.
Asked whether he could go on and win in Paris, Riis was cagey.
"Its two weeks to the finish and there are a lot of good riders in with a chance but with my team doing so well I could do it," the Danish national champion said.
Berzin had looked in charge of the pursuing group, but when young Austrian climber Peter Luttemberger launched a counter-attack he was left at the back. Berzin was then left trailing as he was bereft of any teammates -- a problem which may cost him the Tour.
He lost his two best teammates in the first week when last year's fifth-place getter Ivan Gotti and fellow Italian Stefano Zanini retired injured.
Only Francesco Frattini was capable of rejoining him for the final climb but was quickly dropped.
By contrast, four members of the Mapei team and three Telekom riders managed to stay in the lead group.
Berzin's problems were accentuated by the resurgence of five-time winner Miguel Indurain who took the lead in chasing down Riis and Saturday's stage winner Luc Leblanc -- probably more to make up time on Berzin's lead over him than to try and win the stage.
Indurain now lies eighth, four minutes and 38 seconds behind Riis. His dream may not be over quite yet.
Earlier heavy snow ruled out the climb to the Col de l'Iseran, the highest point of the race at 2,770m, and later the climb to the Col du Galibier was also cancelled because of 100km per hour winds.
The 33-year-old Australian, known as 'Monsieur 100 percent' is often Jalabert's saviour as was the case last year when he led the five man breakaway to Mende giving the French world number one the chance to win on Bastille Day.
Not seeing Stephens with Jalabert on Saturday was reason enough to suspect something was wrong.
Yet on Friday all had seemed on course with the ONCE team all up with the lead group and Stephens as ever leading the pack, blond hair flowing and showing no sign of the terrible day to come on Saturday.
The team did such a good job that Jalabert overtook five-time winner Miguel Indurain of Spain in the overall standings.
Now, however, the team are suggesting that the hard first week allied to Friday's labours cost them on the climbs to Madeleine, Roselend and Les Arcs -- hard to believe that such an expensively assembled team should crack so early on but indicative of the appalling conditions that the peloton has endured on the Tour so far.
Stephens, married and living in Holland, had a fall earlier in the week which may have had a longer term effect on him.
But if there was anyone that Jalabert could have relied on when he was suffering it was Stephens and Spaniard Melchor Mauri, sixth overall last year.
This is not to suggest that Stephens, riding in his fifth Tour, is losing his ability but it symbolised the fracturing of the previously assumed invincibility of the ONCE team -- just as Indurain's immortality was exposed later on in the day.
Stephens has always preferred the role of the domestique (workrider) to being lured to head another team.
"Yeah, sure, I could be team leader in a small team. I would win a few one day races but it doesn't mean a great deal to me. With ONCE I am with the number one team and am highly respected," Stephens admitted.
The ONCE tactics were a little baffling because domestique Patrick Jonker sped off leaving team leader Alex Zulle exposed on the climb to Roselend.
And Jalabert was also to have problems.
He was left with Roberto Sierra, this season's Tour of Rioja winner, and the exceptional Melchor Mauri. But Mauri was dropped by the lead group having made the pace with only Sierra to help as the other members of the 12 man group were not inclined to contribute.
Normally Stephens would have been there to help but for once the Australian hardman was not there and Jalabert's chances were gone.
There is no doubt that Monsieur 100 percent will be back but this Tour has eroded alot of the perceived wisdoms about invincibility from Indurain to the ONCE team.
The harshness of the tour was epitomised by the retirement in tears of the yellow jersey leader Stephane Heulot -- a sure sign that some of the hardest athletes in the world cannot overcome the tough elements and nature will always have its revenge.