A Very Backstreet Holiday was originally scheduled to run on 14/12/12, but it is not listed in ABC’s holiday specials guide.
Shannon Ruth, 39, filed a civil lawsuit in Las Vegas on Thursday. She claimed she was a fan of the 2001 show.
Carter’s lawyer claimed it was “legally unjustified” and “entirely false”.
Variety reported the news that ABC pulled the festive program. The show was filmed in LA this past month. the Hollywood Reporter added that comedy repeats will be shown in its place.
Ms Ruth, a cerebral palsy sufferer and autistic, filed her sexual battery complaint on Thursday. She accused the singer of raping and infecting her with HPV.
Mark Boskovich, her lawyer, said that the assault occurred after she had waited for autographs after a concert in Tacoma (Washington).
Carter claimed that Carter invited her on the bus and gave her a “fun tasting beverage that he called VIP Juice” and instructed her to perform sexual acts on him. He then raped her.
According to the AFP news agency, the lawyer claimed that the singer believed “no one would ever believe” in her because of her disability.
Michael Holtz, Carter’s lawyer, stated in Variety that Carter’s claim regarding an incident that occurred more than 20 years ago was not only untrue but also legally invalid.
“Unfortunately, Ms Ruth has been manipulated into making false accusations about Nick for many years. These allegations have changed over time and materially.
He described the announcement as a “press stunt”, and added: “There is absolutely nothing to this claim, which we have no doubt will be quickly realized by the courts.”
His representatives have been contacted by the BBC.
A Very Backstreet Holiday featured Carter, AJ McLean and Kevin Richardson performing hits from their 10th album A Very Backstreet Christmas. Other stars included Seth Rogen, Meghan Trainor, and Brian Littrell.