On a day when cycling's showcase race crossed into three countries, Valverde crashed in the middle of the main pack of riders, causing a small pileup.
The Tour Web site said he injured his collarbone. Grimacing in pain, he received medical treatment from the Tour doctor before being placed on a gurney.
Kessler is part of the T-Mobile squad that lost its leader, Jan Ullrich, to doping accusations before the race began on Saturday.
Kessler surged ahead of the main pack on the last climb. He held off sprinters who had been favored to win this leg of the three-week race, a hilly route covering Luxembourg, Belgium and the Netherlands.