Byrne was born in Sydney, Australia, the daughter of Jane, a primary school administrator, and Robin Byrne, a semi-retired statistician and market researcher. She attended Balmain Public School and Hunters Hill High School before attending Bradfield Senior College in North Sydney. She has an older brother, George, and two older sisters, Alice and Lucy. She began taking acting classes at age eight, joining the Australian Theatre for Young People and also attended the University of Sydney. In 1999 Byrne studied acting at the Atlantic Theatre Company developed by David Mamet and William H. Macy. Known to family and close family friends as Chabs after a family cat she had in her youth named Chablis, after the wine, a favourite of her native Australia.