In an open letter to The New York Times, Dylan Farrow made her first public comments about the 1992 incident, telling columnist Nicholas Kristof Allen "got away with what he did" and that it "haunted" her.
Ms Farrow, 28, said she was led to comment after Allen was recently honoured with a Golden Globes lifetime achievement award, and said Hollywood's continued embrace of the director worsened her torment.
Allen was investigated for child molestation but was never charged. However, the investigating prosecutor said there was "probable cause".
Representatives for Allen, who has long maintained his innocence, did not immediately return requests for comment.
Ms Farrow wrote: "That he got away with what he did to me haunted me as I grew up. I was stricken with guilt that I had allowed him to be near other little girls."
In the letter, Ms Farrow claims that in 1992 at the family's Connecticut home, Allen led her to a "dim, closet-like attic" and "then he sexually assaulted me". She did not give specifics of Allen's actions but described other abusive behaviour.
She added: "For as long as I could remember, my father had been doing things to me that I didn't like. These things happened so often, so routinely, so skilfully hidden from a mother that would have protected me had she known, that I thought it was normal."
The 1992 allegation came shortly after Allen, then in his mid-50s, became involved with Mia Farrow's adopted daughter Soon-Yi Previn. Allen was not the adoptive father of Ms Previn, who was about 19 at the time. The two married in 1997 and have two adopted daughters.
Though many fans never forgave Allen for his romance with Ms Previn, the director's career was largely uninterrupted. He has continued to release a new film almost every year, with his latest, Blue Jasmine, earning three Academy Award nominations.