The pregnant actress, who has starred in Woody's films such as Match Point and Vicky Cristina Barcelona, called Dylan's action of involving Hollywood actors in the private family matter "irresponsible".
Dylan published a harrowing letter online last month, in which she accused her adoptive father Woody of molesting her as a child. In her message, Dylan condemned Hollywood for staying silent and pointed a finger at actors who had worked with the award-winning director, including Scarlett.
"What if it had been your child, Cate Blanchett? Louis CK? Alec Baldwin?" wrote Dylan. "What if it had been you, Emma Stone? Or you, Scarlett Johansson? You knew me when I was a little girl, Diane Keaton. Have you forgotten me?"
Read Dylan's letter about her experience as a child.
In response, the Lost in Translation actress broke her silence in an interview with The Guardian.
"I think it's irresponsible to take a bunch of actors that will have a Google alert on and to suddenly throw their name into a situation that none of us could possibly knowingly comment on," said Scarlett. "That just feels irresponsible to me."
When asked what she made about the backlash against Woody, Scarlett replied, "I'm unaware that there's been a backlash.
"I think he'll continue to know what he knows about the situation, and I'm sure the other people involved have their own experience with it. It's not like this is somebody that's been prosecuted and found guilty of something, and you can then go, 'I don't support this lifestyle or whatever.' I mean, it's all guesswork."
"I don't know anything about it," added Scarlett. "It would be ridiculous for me to make any kind of assumption one way or the other."
Cate, who this month won the Best Actress Oscar for her role in Woody Allen's film Blue Jasmine, has previously commented on Dylan's letter.
"It's obviously been a long and painful situation for the family and I hope they find some sort of resolution and peace," she said.
Woody has always maintained his innocence and argued that his former partner and Dylan's adoptive mother, Mia Farrow, had influenced her daughter and come up with the allegations out of anger.
Woody responds to Dylan's open letter.
Woody had had an affair with another of Mia's adopted daughters — Soon-Yi Farrow Previn at the time. The filmmaker was in his mid-50s while Soon was a teenager. The couple married in 1997 and have two adopted daughters together.