In a statement, BBC Studios and ABC said: "Brinkley suffered injuries which required surgery to her wrist and arm," keeping her from participating in the competition.
And while the accident left Christie out of the contest, her daughter, Sailor Brinkley-Cook, is stepping into her dancing shoes instead.
Christie broke the news to fans on her Instagram account on Monday.
"I just broke my arm into a 1000 pieces requiring surgery with a metal plate and screws to hold my arm together," she wrote.
She told fans she was devastated to drop out, but happy that her daughter was able to take her place.
"Shattering my arm was quite literally a crushing disappointment, i never ever want to let anyone down...so I looked for a silver lining and i think I found one that is is solid gold! Sailor!"
Season 28 of hit the US show also features Lauren Alaina, Ally Brooke, Hannah Brown, Karamo Brown, Kate Flannery, Ray Lewis, Kel Mitchell, Lamar Odom, Sean Spicer, James Van Der Beek and Mary Wilson in the line up.