"He's going to lose some fitness from this, obviously," Dan Osipow, a spokesman for the U.S. Postal Service pro cycling team, said Tuesday.
The injury, which caused Armstrong to drop out of two races in Europe next weekend, was detected Monday after he had an MRI at a clinic in Monaco. X-rays taken after the Aug. 29 accident and again Saturday were negative.
Armstrong, of Austin, Texas, had complained of pain around his neck, prompting the additional tests. He said he can train "on a limited basis but that is very painful."
"It also makes me nervous when you are out on the open road and it is difficult to turn my neck either way to look at traffic and be aware of what's around," Armstrong said.
Armstrong, 28, is scheduled to compete in the Olympic road race on Sept. 27, and the individual time trial, where he is among the favorites, three days later.
He will miss Saturday's Paris-Brussels race and Sunday's Grand Prix Fourmies, but plans to compete in the GP des Nations, a time trial event, on Sept. 16.
After that, Armstrong will make a final decision on whether to ride in Sydney.
Armstrong was diagnosed, in October 1996, with testicular cancer, which had spread to his lungs and brain. After chemotherapy, he came back to win the 1999 Tour de France and repeated as champion this summer.
In May, Armstrong was hospitalized overnight after crashing in the Pyrenees Mountains of France while training for the tour.
In the latest accident, Armstrong's bicycle was destroyed and his helmet smashed. Olympic and Postal Service teammate Tyler Hamilton of Marblehead, Massachusetts, also was hit but wasn't seriously injured.
"He sounded in good spirits," Osipow said. "I think Lance is always determined in everything he does. This might just be another obstacle for him to overcome."