Buck, who wrote the music for hits like Hey Jack Kerouac and What's The Matter Here, died on Tuesday night at the University of Pittsburgh Medical Center.
10,000 Maniacs publicist Blair Woods said: "He thought he had the flu.
"Then about three weeks ago, he collapsed and his mother found him."
His fellow band members have paid tribute to the guitarist, was aware that he had a problem liver for some years.
Keyboard player Dennis Drew told the Buffalo News: "Rob was a great guitarist and very underrated.
"He had a big influence on other bands. This is a very sad time for all of us.''
Buck was born in New York and started playing guitar at the age of six.
He decided to become a professional guitarist at 16 after seeing The Jimi Hendrix Story.
10,000 Maniacs took their name from the 1964 horror film 2,000 Maniacs.
Buck founded the band with Drew, Steven Gustafson, John Lombardo and Natalie Merchant.
Merchant left the band in 1993 for a solo career and was replaced by Mary Ramsey.
Jack Barton, music director at radio station WYEP in Pittsburgh said: ''10,000 Maniacs was one of the seminal bands that helped form the shape of modern pop in the 90s."
Buck and the band last performed on 6 November at a rally for Hillary Clinton in the US Senate campaign.