Fisher was born in Muscat, Oman, the daughter of Scottish parents Elspeth Reid and Brian Fisher. Her father worked as a banker in Oman for the United Nations at that time. When she was a child, Fisher and her family moved back to their hometown of Bathgate in Scotland, then to Perth, Western Australia, when she was 6 years old. She has four siblings and has said that she had a "great" upbringing in Perth with a "very outdoorsy life. " Fisher has stated that her "sensibility is Australian," she has a "laid-back attitude to life," and she feels "very Australian. " She considers herself a feminist. Her mother and siblings live in Athens, Greece, while her father divides his time between Frankfurt, Germany, and Nicaragua. Fisher attended Swanbourne Primary School and Methodist Ladies' College. She appeared in lead roles in school productions such as Little Shop of Horrors. At 21, she attended L'École Internationale de Théâtre Jacques Lecoq in Paris, where she studied clown, mime and commedia dell'arte.