The 47-year-old singer dated the INXS frontman between 1989 and 1991, and was still a close friend until his suicide in 1997, reported Digital Spy.
Minogue opted for INXS song "Need You Tonight" as one of her choices, before describing Hutchence as "poetic", "tender" and "cultured".
"Professionally, he was so supportive. Someone called me 'the singing budgie' in Australia as a knock. So I did this warm-up gig and we said, 'It's the singing budgie, take that, own it and go out'.
Minogue's current partner Joshua Sasse also read a surprise spoken word poem on the programme.
