The DJ and producer passed away after suffering "a massive coronary" in Guadalajara, Mexico on Thursday, according to BlackBookMag.com.
Kamins produced the Holiday hitmaker's early single Everybody and also dated the pop superstar, and Madonna has now paid her respects to her ex-boyfriend.
In a statement to The Hollywood Reporter, Madonna writes: "I'm very sorry to hear about Mark's death. I haven't seen him for years but if it weren't for him, I might not have had a singing career.
"He was the first DJ to play my demos before I had a record deal. He believed in me before anyone else did. I owe him a lot. May he rest in peace."
Producer Jellybean Benitez writes in a post on his Facebook.com page: "So sad to learn of the passing of Mark Kamins... I will never forget the first time we met and how much we laughed...
"U (you) are and will always be an inspiration to many... I will miss u... Rest in peace my friend."