Johnson, 31, who won this year's NASCAR Nextel Cup, was riding in a golf cart during the tournament in Florida, but was thrown out abruptly when its driver changed direction quickly and landed on his hand - causing the injury.
"I was in a golf cart and the driver took a sharp turn," Johnson said in a statement. "I wasn't holding on tight enough, landed awkwardly on the ground and heard a little pop.
"It was a fluke deal, but fortunately we're in the off-season and I don't plan to miss any additional time."
Race of Champions 2006
Ekstrom wins Race of Champions
16/12/2006 AT 19:47
Johnson was penned in to compete with US Rally champion Travis Pastrana in the Nations Cup section, and to drive in the main event of the night as well.
But despite being ruled out, he will still travel to the Stade de France on Saturday night to cheer on Pastrana and his yet-to-be-named replacement.
"It's disappointing that I can't compete ... but I'll definitely be in Paris to cheer them on and provide any support that I can," he added.
Race of Champions 2006
Loeb cruises into RoC semi-finals
16/12/2006 AT 19:02
Race of Champions 2006
Finland win RoC Nations' Cup
16/12/2006 AT 16:33