The court filing says Whiting and Hussey have suffered emotional damage and mental anguish for decades as a result of the way they were treated.
The film was a huge success at the time, and has been shown to generations of students studying the Shakespeare play since.
It was nominated for four Oscars, including best director and best picture, and won two - for cinematography and costume design.
The lawsuit was filed on Friday in Santa Monica Superior Court under a California law that has temporarily suspended the statute of limitations - which means action cannot normally be taken once a certain time has elapsed - for child sex abuse.
The suspension has led to a host of new lawsuits and the revival of many others that were previously dismissed.
Tony Marinozzi, a business manager for the two actors, told BBC News they had been "betrayed" by the director and the studio.
The pair were unable to take action sooner because they feared there would be ramifications for their careers and that they would not be believed, he said.
"There just wasn't any way for them to tell that story at that time, to get people to listen," he said.
"Now we've seen some movements with #MeToo and other platforms, but at that time there just wasn't a way to tell that story, and it's something that they have had to live with and probably struggle with for a lifetime."
Solomon Gresen, a lawyer for the pair, added in a statement: "Nude images of minors are unlawful and shouldn't be exhibited.
"These were very young, naive children in the 60s who had no understanding of what was about to hit them.
"All of a sudden they were famous at a level they never expected, and in addition they were violated in a way they didn't know how to deal with."
In a 2018 interview with Variety, Hussey defended the nude scene.
"Nobody my age had done that before," she said, adding that Zeffirelli shot it tastefully. "It was needed for the film."
In a separate interview with Fox News, also conducted in 2018, she said the scene was "taboo" in the US, but that nudity was common in European films at the time.
"It wasn't that big of a deal," she said. "And Leonard wasn't shy at all! In the middle of shooting, I just completely forgot I didn't have clothes on." (BBC)
