Brinkley, 65, revealed on "Good Morning America" on Monday that she broke her arm during rehearsals and will need to undergo surgery.
"Showbiz is all about getting a break, and Sailor and I both got one on 'Dancing with the Stars' this season," Brinkley said in a statement on "GMA."
Brinkley-Cook, who is also a Sports Illustrated model like her famous mom, said she's busy learning her mother's dance routine just hours before she will perform live.
"I'm doing this mostly for my mom. I just want to make her happy and make her proud," she said. "She loved doing this. She loves dancing and she loves performing, and getting hurt was her worst nightmare."
ABC and BBC Studios told Fox News on Monday: "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."
Brinkley told People magazine in August that her children had a surprising reaction to their mom joining the competition. Brinkley has three children: Alexa Ray Joel, 33; Jack Brinkley-Cook, 24; and Sailor Brinkley-Cook, 21.
“They laughed,” admitted Brinkley. “They were like, ‘Oh, you’re going to do ‘Dancing with the Stars?’”
While Brinkley’s kids were unsure about their mother’s chances, she told the outlet they were thrilled to learn the names of the other celebrity contenders.
“They got really excited when they started hearing about some of the other people that were coming,” Brinkley explained. “You know, there were like leaks coming out of, maybe there is going to be this person or that, and I know my daughter Sailor is a big Karamo [Brown] fan. So she was like, ‘I’ll be there to visit.’”
Fox News' Stephanie Nolasco contributed to this report.