White said he jammed his wrist Tuesday when he fell on takeoff when he hit a patch of ice, USA Today reported.
"A bit of ice built up that I didn't see. I should have. It was shiny," White said. "It's one of those things that it's going to be annoying, but I don't think it will affect my performance."
His shoulder, jammed in a slopestyle qualifying run, "needs to cooperate a little more. It's a little rough," White said. "I just got to warm it up in the morning."
White is the two-time defending champion in halfpipe and a medal contender in slopestyle. Snowboarding events were added to the Games in 1998.
The opening ceremonies will be Friday and the first of the medal events start Saturday.