Christie Brinkley's arm had "shattered into millions of little pieces"

Speaking to PEOPLE.com, Christie said: "The second I landed, I felt the shards in my arm. Like, I literally felt it in my wrist, and I just instantly looked up and said, 'I'm so sorry, I broke my arm.' There's a little bone at the thumb that usually posts one way. Mine was in the opposite direction. Then there was bone, just it, it was just shattered into a thousand little pieces, just millions of little pieces."

Although she's devastated that she can't compete on the ballroom and Latin show, Christie is excited that her daughter Sailor, 21, has agreed to take her place.

The blonde bombshell said: "Showbiz is all about getting a break, and Sailor and I both got one on 'Dancing with the Stars' this season. Sailor joined the cast when I got mine ... ouch somebody stop me, it hurts to laugh!"

BBC Studios and ABC have wished Christie a "speedy recovery" and confirmed that she needed surgery on her wrist and arm to repair the nasty break.

They said in a statement: "While rehearsing for the premiere of 'Dancing with the Stars', Christie Brinkley suffered injuries which required surgery to her wrist and arm. She is unable to continue her planned participation on the show.

"Keeping it all in the family, her daughter Sailor Brinkley-Cook, a Sports Illustrated model, has chosen to quickly step in with hours to learn the entire routine and will compete in her mother's place for the remainder of the season.

"We wish Christie a full and speedy recovery and look forward to seeing her in the audience, whenever possible, proudly supporting Sailor."