Dushku played the daughter of Schwarzenegger and costar Jamie Lee Curtis in the 1994 film.
In a lengthy post on her official Facebook page over the weekend, Dushku wrote that the stunt coordinator for the film, Joel Kramer, molested her.
"Ever since, I have struggled with how and when to disclose this, if ever," she wrote on Saturday. "At the time, I shared what happened to me with my parents, two adult friends and one of my older brothers. No one seemed ready to confront this taboo subject then, nor was I."
Kramer denied the allegations in an email to CNN, calling them a "a well-crafted fabrication."
"I do not understand what motivated Ms. Dushku to make this statement and I hope that she can find it in her conscious to correct this injustice and return my good name to me," he wrote. "I understand the culture in Hollywood has been historically unfair to women and I applaud and support women who are standing up and pointing out these injustices. It is unfortunate, however that this new culture allows a person to destroy the life and livelihood of a person with false accusations."
On Monday, Schwarzenegger responded to a tweet from "True Lies" costar Tom Arnold, who wrote "I promise you @JimCameron @Schwarzenegger @jamieleecurtis would've done something too. We all love & are proud of @elizadushku #metoo."
"The Terminator" star weighed in with his support.
"Tom, you bet your ass all of us would have done something," he tweeted on Monday. "I'm shocked and saddened for Eliza but I am also proud of her - beyond being a great talent and an amazing woman, she is so courageous."
When contacted by CNN for additional comment, a representative for Schwarzenegger said the tweet speaks for itself. Long before the #MeToo movement, however, the former California governor faced allegations in 2003 that he groped women
in incidents that date back three decades. Schwarzenegger at the time denied some of the accusations and apologized for behaving "badly."
CNN also reached out to Curtis, Dushku and director James Cameron for comment earlier this week. A representative for Curtis told CNN she had no further comment.
Curtis wrote an essay published on Sunday in the Huffington Post
that said Dushku had shared her allegations with her years ago.
"I was shocked and saddened then and still am today" Curtis wrote, before calling on Hollywood to be more protective of young performers.
"The truth will set us all free," Curtis added. "Hopefully that freedom will bring a new ability to call out abuse and, when that abuse occurs, to have swift and consistent action, so that no one again will have to wait 25 years for their truth to be heard."
Kramer is already suffering from the fallout of Dushku's allegations. A spokesperson for Worldwide Production Agency, a company that manages stunt artists and other Hollywood talent and represented Kramer, told CNN in a statement it had dropped him as a client in the wake of the Dushku's allegations.