The Essex-born star, who was best known for starring in an iconic TV ad for Levi’s jeans, was considered a protege of the singer.
Paying tribute on social media, Madonna wrote: “It breaks my heart to know you are gone.
“You were always such a kind sweet human and you suffered too much.
“Hope you are happier wherever you are Nick Kamen.”
The model, who was considered a protege of Madonna, was aged just 18 when he shot the career-changing Levi’s jeans ad.
In the 1985 TV commercial, he is seen stripping off and washing his clothes in front of a host of onlookers in a laundrette to the sound of Marvin Gaye’s 1968 hit Heard It Through The Grapevine.
The ad is regarded as one of the most influential of all time and resulted in an 800 per cent increase in sales of Levi 501s at the time.
Nick caught the eye of many - including Madonna - who wrote and provided backing vocals on his biggest hit, Each Time You Break My Heart, which was originally intended for her True Blue album.
In a BBC radio interview in 1986 Madonna said she was inspired by Nick’s “charisma” and “beautiful voice”.
Other tributes have been paid, including from Nick’s friend Boy George who shared a throwback picture of them together, which he captioned: “R.I.P to the most beautiful and sweetest man Nick Kamen.”
The Great British Bake Off host Matt Lucas wrote: “If you didn’t have a crush on Nick Kamen in the 80s, you probably weren’t there. RIP”
Duran Duran bassist John Taylor said: “So so sad to hear of the passing of Nick Kamen.
“One of the loveliest and gentlest men I ever met.
“He was a beloved friend to my daughter and her Mom. We shall all miss him. RIP Nick”
Nick’ music career spanned four albums between 1987 and 1992. He also enjoyed huge European success with the song I Promised Myself.