An anonymous author wrote the graphic tale, called Girls (Scream) Aloud, which sees the band kidnapped, tortured and worse, reports the Daily Star.
He apparently describes the deaths of each of the singers and tells how their remains are sold on internet auction website eBay.
It purports to be "the very sexy deaths of all five members of the world’s sexiest all-girl group" and warns: "I can not stress enough that this is strictly fictitious."
A spokesman for the band said they were not letting it bother them: "We won’t give this person the satisfaction that the girls care. They have security with them all the time, they are safe enough."
The Internet Watch Foundation, which investigates such material, said it was aware of the site but added: "Because it is hosted in the US, it falls outside our remit, but we are aware of this site. It also contains child abuse fantasy stories.
"We have passed on intelligence reports of the site on to British police for information. And that’s been passed on to the law enforcement agencies in countries where it is hosted."