Stone was born in Scottsdale, Arizona, the daughter of Krista (née Yeager), a homemaker, and Jeff Stone, a contractor. She has a brother, who is two years her junior. Stone's paternal grandfather was of Swedish descent, and his family's surname was anglicized to "Stone" when immigrating to the U.S. through Ellis Island; some of her ancestors also lived in Pennsylvania Dutch Country.
While growing up, she was a member of the Valley Youth Theatre, a regional theater in Phoenix, Arizona, where she appeared in her first stage production, The Wind in the Willows, at the age of 11. Stone attended Sequoya Elementary School and then Cocopah Middle School for sixth grade. She was home schooled for two years, during which time she appeared in 16 productions at Valley Youth Theatre, including: A Winnie-the-Pooh Christmas Tail, The Princess and the Pea, Cinderella, The Wiz, Titanic, Honk!, The Little Mermaid, Schoolhouse Rock Live!, Alice in Wonderland, and Joseph and the Amazing Technicolor Dreamcoat, and performed with the theater's improv comedy troupe.
Stone attended Xavier College Preparatory, an all-girl Catholic high school, as a freshman for one semester. She gave a PowerPoint presentation to her parents, set to the Madonna song "Hollywood", to convince them to let her move to California for an acting career. She dropped out of high school, and in January 2004, moved with her mother to a Los Angeles apartment, at the age of 15. She was then home schooled, so that she could audition during the day.