Craddock, who won the mountains classification at the Settimana Internazionale Coppi e Bartali stage race in March, finished stage 1 on Saturday in last position, 7:50 behind winner Fernando Gaviria.
The American, riding his second Tour de France, crashed into a spectator when avoiding a dropped water bottle at the feed zone in Saint-Vincent-sur-Jard, half-way through the 201km stage from Noirmoutier-en-l'Ile to Fontenay-Le-Comte.
After bravely hobbling the 100km home to the stage finish, Craddock was assessed to have sustained a small fracture of his left shoulder blade, and also required stitches to his left eyebrow, having been left covered covered in blood from the crash.
"Right now, it's extremely painful," Craddock said on the EF-Drapac team website. "It was really painful out on the road just trying to manage it as best I could. I got incredible support from the team to help me to the finish."
"It's difficult. A lot of work goes into these races, especially the Tour," Craddock continued. "Mentally, it's almost harder than physically. I'll try to stay positive, manage the pain as hard as I can. I'm not just going home at the first sign of adversity, so I'll see how I feel tonight [Saturday], how I sleep, how I feel in the morning and get on the bike and see if I can manage it."
"I'm so gutted for Lawson," his Australian teammate Simon Clarke said. "We did all the preparation together for this Tour de France, all the altitude training together. Not only am I rooming with him here at the Tour but we've been living and training together for the last month or so.
"To have this happen to him, I really felt bad for him. I dropped back to give him some words of motivation and support. I encouraged him to get to the finish, cross the finish line and then we could assess things after that, and figure out how bad the damage is."
Craddock added on Twitter on Saturday evening that he would "fight as much as I can to continue", while also pledging $100 for each stage that he could finish to Houston's Alkek Velodrome, which was flooded and damaged as a result of Hurricane Harvey last year.