Cavendish separated the acromioclavicular (AC) joint between his right shoulder and collarbone when he crashed to the ground after colliding with Orica GreenEdge rival Simon Gerrans a little over 200 metres from the line.
The 29-year-old Omega Pharma-QuickStep rider had an MRI scan on the injury last night and planned to make a decision this morning as to whether he would be able to continue in the Tour. "I'm gutted about the crash today," Cavendish said. "It was my fault. I'll personally apologise to Simon Gerrans as soon as I get the chance. In reality, I tried to find a gap that wasn't really there.
"I wanted to win today, I felt really strong and was in a great position to contest the sprint thanks to the unbelievable efforts of my team. Sorry to all the fans who came out to support - it was truly incredible."
Marcel Kittel raced away to take victory but there was carnage in his wake, with Cavendish, who had been trying to achieve his 26th Tour de France stage win, left sitting on the road holding his collar bone.
He then rode gingerly back to the team bus holding his side before being taken away in an ambulance, with his wife Peta Todd and children following in a team car.
It was a sight at odds with the euphoria which had greeted the start of the race in Leeds, with more than a million fans lining the 190.5km route across the Yorkshire Dales to Harrogate.
Omega Pharma-QuickStep had been well positioned entering the final kilometre before Fabian Cancellara (Trek Factory Racing) launched a surprise attack. The sprinters' teams regrouped, though, before Cavendish's crash created chaos.
Kittel powered away to the line ahead of Peter Sagan (Cannondale) and Ramunas Navardauskas (Garmin-Sharp), adding to his four stage wins from the 2013 Tour.
The German, Cavendish's nemesis in last year's event, said he hoped his sprint rival could continue. "I feel sorry for him," he said. "It is something that nobody wants to see, especially in front of his home crowd. I wish him all the best and I hope to see him at the start tomorrow."
While many of those home supporters would have hoped to see Cavendish become the seventh Briton to wear the maillot jaune, the over-riding concern centred on whether he will be able to continue in the Tour at all.
"He is not in great shape, but I am sure he will be OK," said his Australian team-mate Mark Renshaw. "He is a tough guy and it is not the first crash he has ever had."
Omega Pharma-QuickStep team boss Patrick Lefevere was less forgiving of his star rider.
"He was very impatient," Lefevere said. "He wanted to win. He has already done this sprint 100 times in his head before. It's his home tour. He was very focused. Maybe too much. He was so keen to win that he probably made a mistake.
"Gerrans came next to him, slowed down, he wanted to get out, and [Mark] pushed him with his shoulder. Gerrans pushed back and, boom, they crashed."
A victory for Cavendish would have completed a dream day for British cycling fans, with Yorkshire laying on one of the more spectacular Grand Departs of recent years.
Bright sunshine, spectacular scenery and the sort of crowds more usually associated with the high mountain stages combined for the sort of effect organisers would have dreamed of.
The Red Arrows aerobatic jets trailed white, red and blue smoke as the Duchess of Cambridge and Prince Harry performed the ceremonial launch cutting of the tape for the 21-stage, 3,664-km race that will spend three days in Britain before working its way down eastern France to the Alps.
The opening stage was listed as flat, but it was undulating all day in the rolling Yorkshire countryside. Huge crowds lined the roads through picturesque market towns and rolling country lanes flanked by traditional stone walls.
German Jens Voigt (Trek Factory Racing), the oldest man in the peloton at 42 and in his 17th Tour, was in the day's three-man breakaway and distanced Frenchmen Benoit Jarrier (Bretagne-Seche Environnemen) and Nicolas Edet (Cofidis) on the second categorised climb, the Cote de Buttertubs.
Voigt held a three-minute advantage with 70km of racing remaining and secured the polka-dot King of the Mountains jersey at the final climb of Cote de Grinton Moor before being caught by the peloton with 60km to go.
Earlier, Team Sky's defending champion Chris Froome was roared off as the cream of world cycling left Leeds city centre before making their way to the official start at Harewood House.
The main contenders for the race, Britain's Froome, Alberto Contador of Spain and Italian Vincenzo Nibali, were all comfortably tucked into the pack.
Froome avoided the carnage which engulfed Cavendish to finish sixth. "It was perfect, really," Froome's Team Sky colleague Geraint Thomas said. "We stayed out of trouble. Mission complete for day one."