Van Garderen went down after touching wheels in the peloton with 35km to go but it was a second incident after he had remounted and was chasing back on that put in out of the WorldTour stage race.
According to a BMC Racing press release, Van Garderen ran into another team car and suffered a neck sprain, commonly referred to as whiplash in addition to other minor injuries.
BMC Racing Team doctor Dr. Michel Cerfontaine said that Van Garderen avoided any fractures or concussion.
"He has some abrasions on his forehead and left hip. Normally, Tejay can start training in 3-4 days and in one week, he will have another X-ray to determine how the sprain is healing. We will continue to monitor his progress over the coming days," he said.
After missing out on the Tour de France last season, Van Garderen had a solid Vuelta a España, finishing 10th overall. He finished third overall in the Volta ao Algarve in his season opener, and had ambitions for Paris-Nice having been named as the BMC team's outright leader for the race.
"I'm really disappointed. I had good form at Volta ao Algarve and I was hoping to be able to capitalize on that," Van Garderen said. "Hopefully, I can get back on the bike soon, keep moving forward and maybe look at the race program to make up for the missed days here. It's only March 4th so there are plenty of races to come."
He explained that the first crash was minor and came when the peloton was fighting for position. "My tire was caught on a lip. The roads were wet and my wheel slipped out. I was able to get back up, and get going but I had trouble putting my chain back on and I noticed other damage with my gears and a puncture, so I thought I would have to change bikes.
"I was looking down to see what the damage was and next thing I knew I was on the ground as I had crashed into the back of a team car that had stopped on the road. I don't know if anyone was at fault as they had stopped for their rider."
The second impact, which happened out of view of the television cameras, knocked the wind out of him.
"I couldn't breathe. I also had pain in my upper back and neck so I couldn't really sit up. When the medics arrived and saw my helmet smashed and that I was having trouble breathing, they put me straight into the ambulance," he said.
"After a few minutes, I realized it wasn't so bad. The medics went through some concussion protocols and I didn't show any signs of concussion. Fortunately, X-rays showed no fractures. It's good to take precautions but in the end, maybe I could have been able to continue. I have pain in my neck and a bit of a headache, but I don't feel nauseous."