Born in Belgrade, Serbia, Dravić became involved with performing arts at the age of four via her parents enrolling her in a dance program.

[3] In 1959, still a high school student, Dravić got spotted by director František Čáp[4] who approached the eighteen-year-old about being in his film Vrata ostaju otvorena after seeing her on the cover of a youth magazine in a ballet dancers' group photo.

Her big break came in 1962 in Branko Bauer's Prekobrojna for which she won the Golden Arena for Best Actress (Yugoslav equivalent of an Academy Award).

The memorable role, as well as the much-publicized accolade, propelled her to becoming Yugoslavia's first and arguably biggest female movie star.

She was memorable and believable, whether as the tragic heroine in state-sponsored World War II epics, the eccentric protagonist of experimental arthouse films like WR: Mysteries of the Organism or in romantic comedies.