Froome was at a safe distance behind, much to his relief.
"That's everyone's worst nightmare. Fortunately I was to the side of that crash and went around it no problem," Froome said. "I'm feeling really good. Today was a great day for us, staying out of trouble, staying at the front."
Kittel won the opening stage and is now the first rider to capture two stages in this year's race.
"Things went very well with my team today," he said. "I managed to get on Greipel's wheel and overtake him."
Veelers was not seriously harmed and was later able to answer questions outside the team bus.
"I had the feeling Cavendish was boxed in my wheel," Veelers said. "He touched my handlebars and knocked me over."
Peter Sagan, who won the green jersey for best sprinter in last year's Tour, finished the stage in fourth.
The finish looked tailor-made for Cavendish, who was going for his 25th career Tour stage win to tie Frenchman Andre Leducq for third place on the all-time list of Tour stage winners. As the British rider moved into position to attack before the final corner, Cavendish appeared to lean into Veelers and send the Argos-Shimano rider flying off his bike. Race stewards were examining what happened. Following a rest day, the 122-mile flat ride started from Saint-Gildas-Des-Bois in northwest France and finished in the walled port city of Saint-Malo, a tourist destination on the coast of Brittany.
1. C. Froome
2. A. Valverde -1:25
3. B. Mollema -1:44
4. L. ten Dam -1:50
5. R. Kreuziger -1:51
6. A. Contador -1:51
Tour de France
O Wednesday, 6 a.m.
TV • NBCSN