"We've made a decision to disqualify Peter Sagan from the Tour de France 2017 as he endangered some of his colleagues seriously in the final metres of the sprint which happened in Vittel", said the president of the race commission Philippe Marien.
He cited Article 12 of the International Cycling Union (UCI) rules, which states that any rider making a wilful obstruction "against one of the 1st 10 riders placed" faces elimination.
He was trying to follow the wheel of the eventual stage victor, France's Arnaud Démare, by squeezing between Peter Sagan and the barrier, and as Cavendish tried to make space, Sagan bumped into him, sending the Manxman into the barrier.
Cavendish did finish the stage but later left his Dimension Data team bus with his arm in a sling as he was taken to hospital by ambulance.
"Like I said, I get on with Peter, a crash is a crash, but I'd like to know about the elbow".
His crash came on a bend just inside the final kilometre but Cavendish's fall looked more damaging, just inside the final 100 metres.
After the crash, Sagan went over to see how Cavendish was and patted him on the back, while the British rider showed him his wounds.
The 50 points for winning also put him in contention to claim the green jersey for sprinters.
Demare took the green jersey for the points classification and is now the favorite to take it to Paris, a feat Sagan was looking to achieve for a record-equalling sixth time.
Geraint Thomas finished eighth, two seconds behind the victor, to hold on to the race leader's yellow jersey. "He came to me and I had to defend".
German sprinter Andre Greipel finished third and had strong words for Sagan. "I'm not a doctor, but from the feelings I'm not optimistic". "I tried to take off quite a lot of speed, but there was nowhere to go".
Then Cavendish fell hard on his right shoulder just before the finish line.
The 27-year-old Slovak, who rides for Bora-Hansgrohe, powered over the line in front of Australia's Michael Matthews, with Ireland's Dan Martin third.
"After Richie Porte attacked I chose to go and I said to myself I was going too early", said Sagan.
Thomas scraped his knee but said it was OK.
Starting from Verviers, the native town of Ronde van Vlaanderen and Amstel Gold Race champion Philippe Gilbert, stage 3 of the Tour de France saw the riders make a foray into Luxembourg before arriving in France for the first time this year, three days after the Grand Depart in Düsseldorf.
The race goes into the hilly Vosges region with a 160.5km stage from Vittel to la Planche des Belles Filles, a relatively new climb that's been used in the race just twice: in 2012 and 2014.