"Olivia was a remarkable person whose warmth, wisdom, and pure kindness touched the lives of all who knew her," her family said in a statement posted to her Instagram account.
Buenos Aires-born Hussey was 15 when she and her co-lead Leonard Whiting starred in the Oscar-winning adaptation of William Shakespeare's tragedy.
In 2023, the two actors filed a lawsuit against the studio alleging child abuse over a controversial nude scene featuring the pair, who were minors at the time.
A judge dismissed the lawsuit later that year.
In a 2018 interview with entertainment trade publication Variety, Hussey said Zeffirelli had shot the nude scene tastefully.
"Everyone thinks they were so young they probably didn't realize what they were doing," Hussey said.
"But we were very aware. We both came from drama schools and when you work, you take your work very seriously."
Whiting told Variety the pair had supported each other through the daunting experience.
"Olivia was very, very nervous and frightened as well, but we really were very fond of each other and we helped each other get through the whole thing," he said in 2023.
Born to an Argentine opera singer and a British legal secretary, Hussey moved with her family from Buenos Aires to London when she was seven years old.
She studied at the Italia Conti drama school and was already a working actor as a teenager when she was cast in Zeffirelli's film.
Hussey, who received a "New Star of the Year" Golden Globe for her performance, would later star in the 1974 slasher film "Black Christmas" and the 1978 adaptation of Agatha Christie's "Death on the Nile", among other projects.
She is survived by her husband David Eisley, their three children and a grandchild.
