Slayer spokeswoman Heidi Robinson-Fitzgerald said Hanneman died Thursday morning of liver failure at a Los Angeles hospital with his wife, Kathy, by his side.
The guitarist had recently begun writing songs with the band in anticipation of recording a new album later this year. He had been slowly recovering from what was believed to be a spider bite that nearly cost him his arm after he failed to seek immediate treatment.
"The music industry has lost a true trailblazer, and our deepest sympathies go out to his family, his bandmates and fans around the world who mourn his untimely passing," said Neil Portnow, president and CEO of the Recording Academy, in a statement.
Robinson-Fitzgerald said it's believed the spider bite contributed to the failure of Hanneman's liver, but it is unclear whether an autopsy will be scheduled. No funeral arrangements have been made.
"Jeff Hanneman will always be a metal god," rocker Andrew W.K. posted on Twitter.
Hanneman co-founded the thrash metal pioneers in Huntington Beach, Calif., in 1982.
AP Music Writer Chris Talbott contributed to this report from Nashville, Tenn.