The stand-up special Bill Cosby 77 was due to premiere on 28 November in the US, but the streaming service has decided to postpone the launch.
A Netflix spokesperson said: “At this time we are postponing the launch of the new stand-up comedy special Bill Cosby 77.”
The hour-long special was due to air in honour of Cosby’s 77th birthday.
Netflix’s announcement came hours after supermodel Janice Dickinson alleged Cosby had drugged and raped her in 1982 in an nterview on Entertainment Tonight.
The 59-year-old said Cosby had offered to help her with her career, and that during their meeting they discussed a possible role for her on his hit sitcom The Cosby Show.
Bill Cosby: Career in pictures
Bill Cosby: Career in pictures
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Winner of his first Emmy for 'I Spy' is Bill Cosby being congratulated by his wife Camille held at Americana Hotel, 1966
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Bill Cosby in 'I Spy', 1960s
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Bill Cosby in July 1973 in Perth
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Bill Cosby and Richard Pryor in 'California Suite', 1978
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Bill Cosby and Elmo in Sesame Street, 1989
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Bill Cosby poses for a picture with Florence Griffith-Joyner in June 1989
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Comedian Bill Cosby back in 1992
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A scene from a 1992 episode of 'The Cosby Show'
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US Monica Seles breaks into laughter as she jokes with comedian Bill Cosby during a celebrity match in the stadium at the US Open for the Arthur Ashe AIDS Challenge on 27 August 1995
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Bill Cosby meets Toronto Blue Jays' All-Star Joe Carter after the Stars played the Stripes in the Celebrity All-Star game which preceded workouts for the 67th All-Star Game at Veterans Stadium on 8 July 1996 in Philadephia
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Co-hosts Oprah Winfrey and Bill Cosby joke with each other during the opening of the 2000 Essence Awards 14 April 2000 at Radio City Music Hall in New York City
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Bill Cosby jokes with baseball great Hank Aaron after they both received the Presidential Medal of Freedom Award from U.S. President George W. Bush during a ceremony on 9 July 2002 at the White House in Washington
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Bill Cosby poses backstage after winning the 'Bob Hope Humanitarian Award' during the 55th Annual Primetime Emmy Awards at the Shrine Auditorium on 21 September 2003 in Los Angeles
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'Tonight Show' host Jay Leno and comedian Bill Cosby laugh during a surprise visit by Cosby to sign a Harley-Davidson motorcycle that Leno is using to raise money for the victims of Hurricane Katrina at NBC studios on 9 September 2005 in Burbank, California
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Bill Cosby speaks during a taping of 'Meet the Press' at the NBC studios on 14 October 2007 in Washington
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Bill Cosby at the 12th annual Mark Twain Prize for American Humor at the John F. Kennedy Center on 26 October 2009 in Washington
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Bill Cosby speaks at the National Action Network's 20th annual Keepers of the Dream Awards gala in New York on 6 April 2011
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Bill Cosby during the 100th anniversary celebration of the Beverly Hills Hotel & Bungalows supporting the Motion Picture & Television Fund and the American Comedy Fund, 2012
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Bill Cosby speaks onstage at the Thurgood Marshall College Fund 25th Awards Gala on 11 November 2013 in Washington
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Bill Cosby performs at the Treasure Island Hotel & Casino on 26 September 2014 in Las Vegas
She claimed he offered her wine and a pill to alleviate her period pains.
“The next morning I woke up, and I wasn’t wearing my pyjamas, and I remember before I passed out that I had been sexually assaulted by this man,” she said.
Cosby has consistently strongly denied all the previous sexual allegations levelled against him, which his attorney has described as “bizarre”.
Last week the Washington Post published an article by former model Barbara Bowman, in which she accused Cosby of having “drugged and raped” her in 1985, when she was 17.
Another alleged victim, publicist Joan Tarshis, claimed she was sexually assaulted by the comedian in 1969.
Earlier this week, Cosby’s lawyer John Schmitt said the comedian would not “dignify the allegations with a response”.
In a statement, he described the women’s allegations as “decade-old” and “discredited”, adding: “The fact that they are being repeated does not make them true. Mr Cosby does not intend to dignify these allegations with any comment.”