The magician raped the 22-year-old victim, sexually assaulted her on two other occasions and threatened to kill her, court papers filed in Washington state claim.
The woman says her nightmare unfolded two summers ago, when the 52-year-old performer invited her to his $50 million private retreat on Musha Cay after meeting her at a show in Washington state.
One of the showman's assistants invited the alleged victim backstage, where she was told about promotional work on the island that might lead to "modeling opportunities," according to the suit, filed on July 29.
When she arrived on the island, which is reachable only by private boat, on July 27, 2007, "she realized no one else was in attendance other than . . . Copperfield," the suit says.
After the two dined, they went to the magician's room to watch a movie.
"Copperfield then attacked [her] and sexually assaulted her" and "threatened to kill her," despite the victim's attempt to fight him off, leaving her "extremely traumatized," her filing charges.
Without cellphone coverage on the island, the woman tried to use a land line to call her boyfriend, but Copperfield -- once married to model Claudia Schiffer -- allegedly marched in, holding a phone to his ear as if he were "listening to her call."
The next morning, she claims, he took her to a private beach, "ordered her to get naked," and held her head under water, telling her, "This is an example of what you will get if you tell anyone," before sexually assaulting her twice more.
The US Attorney's Office has not filed criminal charges, but a grand jury has been convened, according to the Seattle Times.
The woman is seeking unspecified damages.
"This lawsuit is extortion for money, plain and simple," Copperfield's lawyers said in a statement.
"Unfortunately, false claims like this only hurt the women who really have been abused."