Asheton, 60, was found on his couch and appeared to have been dead for several days, Ann Arbor Police Sgt. Brad Hill said.
"We do not expect foul play," Hill said.
Stooges frontman Iggy Pop, who went on to enjoy a successful solo career, said in a statement that he was in shock about the death of "my best friend."
The Stooges formed in 1967, with the lineup rounded out by Asheton's brother Scott on drums and the late Dave Alexander on bass. Known for a violent and primitive style that featured stage-diving and outrageous antics by Pop, The Stooges were part of a late 1960s Detroit-area rock scene that also included the MC5.
They broke up in 1974 after three now-classic albums, limited commercial success and mounting drug problems for Pop.
But backed by Asheton's guitar riffs on songs such as "I Wanna Be Your Dog" and "TV Eye," the band's music has been credited as a powerful influence on a wide range of punk and alternative bands including The Sex Pistols, The Ramones and The White Stripes.
"As a musician Ron was The Guitar God, idol to follow and inspire others," Pop and the Stooges said in a statement. "That is how he will be remembered by people who had a great pleasure to work with him, learn from him and share good and bad times with him."
After The Stooges broke up, Asheton acted in a series of low-budget horror films in the 1980s and 1990s.
Asheton, ranked as the 29th greatest rock guitarist by Rolling Stone, rejoined The Stooges when the band reunited in 2003 and for the 2007 comeback album, "The Weirdness."
The band has been nominated for induction into the Rock and Roll Hall of Fame.
(Reporting by Kevin Krolicki; editing by Mohammad Zargham)
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