Vande Velde was among three team riders, including American Tyler Farrar and New Zealand's Julian Dean, from the team who were taken to hospital for checks after dozens of competitors crashed on the slippery descents in the latter half of the 201km ride from Brussels to Spa in the Belgian Ardennes.
The 34-year-old Vande Velde had finished fourth on the Tour de France in 2008 and eighth in 2009 and had high hopes for this year's race.
A team statement said that Vande Velde's absence would mean a total change of strategy.
"Clearly, this will mean a change in the general strategy for Team Garmin-Transitions. We'll be looking for stage wins and ways to animate the race," said team chief Jonathan Vaughters.
Farrar and Dean suffered heavy bruising but should be fit to start Tuesday's third stage, however Farrar could be in pain.
"Tomorrow(Tuesday) is going to be painful for Tyler," added Vaughters.
"He's got significant injuries, so starting alone is a huge step, and from there we’ll have to see how he goes."
Spilled oil from a motorbike which crashed ahead of the peloton is being blamed for the high number of accidents, with seven-time winner Lance Armstrong, reigning champion Alberto Contador and last year's runner-up Andy Schleck all escaping unhurt despite hitting the tarmac.
Garmin's David Millar of Scotland and South African Robbie Hunter were also involved in spills although they did not need hospital treatment.
Vande Velde said he crashed twice, the second time leaving him in a ditch.
"I'm not sure what I hit; I think it might have been a pole," said the American.
"At that point my eye was bleeding pretty badly and the pain in my side and my back was excruciating. I got back on the bike though... I tried to stay with that group, but the pain was too much and I couldn’t get out of the saddle to make it back on."
He added: "No one wants to leave the Tour de France. I'm indescribably disappointed to not be starting tomorrow(Tuesday). I don’t ever want to have to see another day like today, whether I’m in the race or not."
Millar said: "Today was definitely in my top five worst days on a bike, ever, and that's a big cull considering the length of my career.
"Within only 200 meters of cresting I could see Lance (Armstrong) fall about 10 places in front of me on a straight road.
"When I saw that happen I knew something wasn't right -- and that was immediately followed by my wheels disappearing from under me and my sliding across the ground.
"Only 200 meters after getting back on my bike I was faced with a Cofidis rider losing control in front of me. There was nothing I could do and I hit him and somersaulted over my handlebars, landing heavily on my ribs in a ditch thinking this time, I wasn't fine.
"I got up and fixed my bike myself, and then I tip toed down the descent surveying the absolute carnage that was the Tour de France peloton and wondering what was going on."
Numerous spills also marred the first stage on Sunday but the peloton is facing more carnage in the third stage Tuesday which features seven treacherous cobblestone sectors.