Campbell was born in Guelph, Ontario. Campbell's mother, Marnie (née Neve), is a yoga instructor and psychologist from Amsterdam, the Netherlands. Her father, Gerry Campbell, an immigrant to Canada from the East End of Glasgow, Scotland, taught high school drama classes in Mississauga, Ontario — first at Westwood Secondary School (now Lincoln M. Alexander Secondary School) and later at Lorne Park Secondary School. Campbell's maternal grandparents ran a theatre company in the Netherlands and her paternal grandparents were also performers. Campbell is Catholic, but also identifies as Jewish because of her mother's Sephardic Jewish ancestry, about which she has said: "I am a practising Catholic, but my lineage is Jewish, so if someone asks me if I'm Jewish, I say yes".

Campbell's parents divorced when she was two years old. She and brother Christian resided largely with their father (who received custody of the two), with regular periods at their mother's home, until Neve move