"She had leukaemia, when I was making the movie The Boxer with Daniel Day Lewis, three weeks from the end I had to leave because she'd been diagnosed with leukaemia, they thought she wasn't going to get better but she fought back and she won it," he said.
"She had two years of chemo, she was good, she came back."
When the Irishman started becoming visibly upset, his campmates offered their support.
"You're a man going through pain and you're vulnerable about it, that takes strength. There is no rules to grieving... it's a reflection of your love," N-Dubz star Tulisa Contostavlos said.
"It was hard for weeks in the hospital, just watching, shocking," McGuigan said tearfully.
"Thank you, you're all so lovely, I really appreciate it," he added.
McGuigan, a former professional boxer who became World Featherweight Champion in 1985, is on the 24th series of the reality TV show alongside celebrities including Danny Jones from McFly, TV presenter Jane Moore and Coleen Rooney.
Later in the episode, Rooney, who is married to ex-England footballer Wayne Rooney, became emotional over the loss of her sister Rosie, after McGuigan spoke about Danika.
"She was 14 when she died, she'd be 26 now. It's hard to lose a child, I've always said that... so we're lucky to have what we've got," she said.
Rosie had a rare genetic disorder called Rett syndrome.
At the time of her death in 2013, Rooney posted a tribute on social media, writing that she and her family were "absolutely heart broken to have lost our angel Rosie... we love you more than words can say."
Rett syndrome is a neurological disorder that causes profound physical and communication disabilities. It affects around one in 10,000 girls born each year and rarely occurs in boys.
