Madsen died on Thursday morning from cardiac arrest, his manager, Ron Smith said.
He appeared in dozens of films during a career that spanned more than 40 years, with screen credits including Thelma and Louise, Free Willy, Donnie Brasco and Sin City.
But he was well known for his collaborations with Tarantino, who cast him in Reservoir Dogs, Kill Bill: Vol. 2, The Hateful Eight and Once Upon a Time in Hollywood.
Tributes poured in for Madsen on social media.
Captain America co-director Joe Russo said: “Michael Madsen ALWAYS had bite. RIP.”
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