Burke, 31, said the abuse started when she was in kindergarten.
She didn't name anyone specifically, but said, "He would make me watch pornographic videos. He was kind of like that fatherly figure – I think he knew my weakness, that I was very insecure. He knew that no one was ever around," according to People magazine's recap of the Sunday special.
Burke, 31, said her parents had divorced and her father had moved away, so this man was tasked with watching her and took advantage.
"I couldn't speak up for myself. It was hard for me to say no. In a weird way, it was like I didn't want to hurt him," the native Californian added.
The dancing star eventually had to testify against the man when she was 6, she said.
"My mom was there holding my hand, I was shaking and there was my molester right in front of me. It was so terrifying to see him face to face. I remember taking a lot of breaks because I would just break down," she said, adding it was dance that brought her back.
"I was able to start building my confidence and know that I don't need anybody to be happy. I just needed just me. I needed to know that I could do this on my own," she continued. "I'm proof that you can actually move on from this."
This isn't the first time Burke has spoken out about the past abuse. In 2011, she revealed that abuse, along with past physical altercations at the hands of former boyfriends, in her book, "Dancing Lessons."
"I'm telling my story," she told People at the time. "They're not secrets. There's no shame."
The Sunday special also featured the Duggar family after it was revealed earlier this year that Josh Duggar, a former star on the TLC Network, had inappropriately touched minor girls, including his sisters, years ago starting when he was 14.