Izzo was born in Santiago, Chile,[5] to Chilean model Rosita Parsons [es].[4] She is of Italian descent on her father's side. She has a younger sister, Clara Lyon Parsons, who is a model as well.[6] When she was twelve, she moved to Atlanta with her father, who was working towards a Ph.D. at Georgia Institute of Technology. She was bullied over her strong Chilean accent, but said she "got over [her] accent pretty fast" after watching the 2002 sports filmBlue Crush several times. She recalls becoming "obsessed with Blue Crush star Kate Bosworth."[5]
In 2010, she made her acting debut in Instrucciones para mi funeral (Instructions for my Funeral), an independent film made by Sebastián Radic as a graduation project.[8]
Izzo's modeling career reached its peak in 2011 when she and her mother were invited to São Paulo Fashion Week, where they met Gisele Bundchen. It resulted in Izzo becoming the new face of Colcci, a Brazilian fashion company.[7] That year, Izzo appeared in Que pena tu boda [es] (Sorry About Your Wedding) a comedy by Chilean director Nicolás López.[9]
In 2012, with one commercial feature movie to her name and three more about to be released—Que pena tu familia (What a Pity About Your Family), Aftershock, and The Green Inferno (directed by her then-future husband, now ex-husband, Eli Roth)—Izzo moved to Los Angeles, when she soon secured small roles in Hemlock Grove and the failed television pilot I Am Victor.[10]
On November 8, 2014, Izzo married American actor and director Eli Roth on the beach of Zapallar, Chile.[12] They were introduced by mutual friend and director Nicolás López during the production of 2012's Aftershock.[5][13] López was unaware Izzo could speak English, and she originally had a small role in the film. When he learned she could speak English fluently, Roth cast her in the lead, where they "spent the whole shooting process together". She attributes the start of their relationship to "the randomness of the world".[5] They filed for divorce in July 2018; it was finalized in August 2019.[14]