Dylan, who is now married and living in Florida under a different name, has written an open letter to The New York Times. Speaking to columnist Nicholas Kristof, the 28-year-old said that she decided to tell her side of the story about the director so loved by Hollywood.
Last month, Woody was given a lifetime achievement award at the Golden Globes, which was applauded by some and criticised by others including Dylan and her adoptive mother Mia Farrow.
Mia Farrow, Dylan Farrow and Woody Allen
"That he got away with what he did to me haunted me as I grew up," wrote Dylan. "I was stricken with guilt that I had allowed him to be near other little girls.
"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.
"That torment was made worse by Hollywood. All but a precious few (my heroes) turned a blind eye. Most found it easier to accept the ambiguity, to say, 'who can say what happened,' to pretend that nothing was wrong.
"Actors praised him at awards shows. Networks put him on TV. Critics put him in magazines. Each time I saw my abuser's face — on a poster, on a T-shirt, on television — I could only hide my panic until I found a place to be alone and fall apart."
At the time of the alleged abuse, Dylan was seven years old. Woody was taken to court and accused of "inappropriately touching" his adopted daughter, who Dylan recounts was a case of "sexual assault."
The claims were investigated and Connecticut state attorney Frank S. Maco announced that while he found "probable cause" to prosecute Woody, he decided to drop the case because Dylan was too "fragile" to withstand a trial.
Mia, who Frank claimed agreed with him on dropping the charges, won custody of the children in 1993 and denied Woody visitation rights with Dylan.
Woody reportedly claimed that Mia had come up with the allegations out of anger, after he had had an affair with another of Mia's adopted daughters — Soon-Yi Farrow Previn. Woody was in his mid-50s while Soon was a teenager. The couple married in 1997 and have two adopted daughters together.
Woody has long maintained his innocence and while many fans never forgave the director for his romance with Soon, the Hollywood star has continued to release films with his latest Blue Jasmine earning three Academy Award nominations.
Woody and Soon-Yi Farrow Previn
Dylan told columnist Nicholas, who is close friends with Mia, said that she was speaking out now to set the record straight and give courage to victims of sexual abuse.
"I know it's 'he said, she said,'" Dylan told Nicholas. "But, to me, it's black and white, because I was there. I was thinking, if I don't speak out, I’ll regret it on my death bed."
"This time, I refuse to fall apart," wrote Dylan in her letter. "For so long, Woody Allen’s acceptance silenced me. It felt like a personal rebuke, like the awards and accolades were a way to tell me to shut up and go away.
"Today, I consider myself lucky. I am happily married. I have the support of my amazing brothers and sisters. I have a mother who found within herself a well of fortitude that saved us from the chaos a predator brought into our home."