One of the star's breakthrough movie roles was in an Allen film, 2008's Vicky Cristina Barcelona, and she spoke in an Instagram post about the thought processes that brought her to her decision.
The allegations resurfaced with Farrow's open letter in 2014, and again last year in the wake of the #MeToo movement, prompting Greta Gerwig and Dave Krumholtz to say they regret working with the director.
"The day after the Weinstein accusation broke in full force I was shooting a day of work on Woody Allen's latest movie in New York," Hall has now said.
"I couldn't have imagined somewhere stranger to be that day. When asked to do so, some seven months ago, I quickly said yes.
"He gave me one of my first significant roles in film for which I have always been grateful, it was one day in my hometown – easy."
She continued: "I have, however subsequently realized there is nothing easy about any of this.
"In the weeks following I have thought very deeply about this decision, and remain conflicted and saddened.
"After reading and re-reading Dylan Farrow's statements of a few days ago and going back and reading the older ones - I see, not only how complicated this matter is, but that my actions have made another woman feel silenced and dismissed."
Hall added: "That is not something that sits easily with me in the current or indeed any moment, and I am profoundly sorry.
"I regret this decision and wouldn't make the same one today. It's a small gesture and not one intended as close to compensation but I've donated my wage to @timesup.
"I've also signed up, will continue to donate, and look forward to working with and being part of this positive movement towards change not just in Hollywood but hopefully everywhere. #timesup"
Dylan Farrow welcomed Hall's announcement and posted her thanks on Twitter.
She later added: "There have been some brave and bold women who have taken a stand with and for me in the past few days.
"I want to acknowledge their integrity, their courage, and their exemplification of a new way forward. Thank you, it means the world. #TIMESUP"
There have been some brave and bold women who have taken a stand with and for me in the past few days. I want to acknowledge their integrity, their courage, and their exemplification of a new way forward. Thank you, it means the world. #TIMESUP- Dylan Farrow (@realdylanfarrow) January 13, 2018
Time's Up, which organised the all-black red carpet at the 2018 Golden Globes, has also created a legal defence fund for lower-income women seeking justice for workplace sexual harassment and assault.
It is also advocating for a change in the law to punish companies that tolerate persistent harassment, and push for equal gender representation in studio and talent agencies.
After Mark Wahlberg was widely criticised for negotiating a $1.5 million reshoot fee for Ridley Scott's All the Money in the World, he donated his fee to Time's Up, with an additional $500,000 being donated by his agency WME.
The reshoots were necessary after Kevin Spacey, the subject of several allegations of sexual assault and misconduct, was replaced in the film by Christopher Plummer, despite the original version of the film having been fully shot, edited and ready for festival release.
While Wahlberg had negotiated an additional salary for the nine-day reshoot, director Scott and co-star Michelle Williams did the re-shoot for free, only receiving per diem living expenses.
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