The 41-year-old shed tears from her seat on the judging panel after one of her contestants, Dami Im, performed the classic Simon & Garfunkel track.
"I've had the roughest week ever, that was for my parents and my grandfather, that song tonight," Dannii said after watching her protégé.
"I've had the toughest time. You have been my absolute angel. And for anyone else out there who has ever had a tough time — that is your song."
She was comforted by her fellow judges, Ronan Keating, Natalie Bassingthwaighte and LMFAO frontman Redfoo, who all rallied around the mum-of-one.
Dannii and Redfoo didn't see eye-to-eye on the performance, with the latter claiming he had only heard the track "maybe three times in my life", and saying that the song was lacking something.
But after Dannii, 41, gave her feedback to Dami, all three of her co-judges were quick to console her.
Dannii later posted a picture taken with her contestant on her Tumblr page, writing, "Dami's song this week, Bridge Over Troubled Water, was for anyone going through a tough time or anyone who needs to feel a little hope.
"Dami helped me dedicate this performance tonight to my family and my beautiful Grandmother who just recently passed away."
Dannii Minogue posing with Dami
It is thought that the Minogue family lost their beloved matriarch two weeks ago, reportedly after a battle with cancer.
The loss has remained largely out of the public eye, but Dannii is said to have reflected on the devastation of her grandmother's death at Ronan's charity fundraiser, The Emerald & Ivy Ball, in honour of the Cancer Council, in Sydney on Friday night.
Dannii's courageous sister Kylie, 45, won her fight with breast cancer, after being diagnosed in 2005, inspiring thousands of woman to seek testing for the disease.