"Hanneman was in an area hospital when he suffered liver failure," the band said.
The guitarist had been recovering from a spider bite which had left him with necrotising fasciitis, a flesh-eating disease which attacks subcutaneous tissue.
Hanneman founded Slayer with fellow guitarist Kerry King in the early 1980s in suburban Los Angeles.
The band was known as one of the "big four" thrash metal groups of the 1980s, along with Anthrax, Megadeth and Metallica.
Hanneman is best known as a writer of the songs Raining Blood and Angel of Death from the 1986 album Reign in Blood, which is considered a landmark of the thrash genre.
Fellow musicians took to Twitter to express their grief. Slash, guitarist with Guns 'n' Rose, said: "Tragic & shocking news about Jeff Hanneman. He is going to missed by so many. What a sad day for Metal. RIP man", while Andrew WK said "Jeff Hanneman will always be a metal god. A true master, he gave energy and excitement to millions, and will continue to."
Hanneman is survived by his wife, Kathy, and three siblings."
in The Guardian, 03rd of May 2013. read it here here.
"Hanneman fell seriously ill in 2011 after he was bitten by a spider - he almost lost his arm and was placed in a medically-induced coma. The star subsequently underwent several operations to remove the dead and dying tissue from his arm and pulled out of Slayer's 2012 tour dates to continue his treatment.