Appleby was born in Los Angeles, California, the daughter of Dina (née Bouader), an Israeli-born Hebrew school teacher, and Jerry Appleby, a Jewish-American telecommunications executive. She and her younger brother, Evan, were raised in Calabasas, in Los Angeles County. Her mother is of Sephardic Moroccan Jewish background. In Hebrew, "Shiri" means either "my song" or simply "sing". She has a scar above her left eyebrow, resulting from a dog bite when she was young. To get over her fear of dogs, she went on the show Emergency Vets, accompanying staff veterinarian Dr. Kevin Fitzgerald (she also overcame another phobia in the same episode by holding a live snake, one of Fitzgerald's patients) and shortly after adopted a Tabby, which she named Abby.

Appleby graduated from Calabasas High School in 1997 and went on to major in English literature at the University of Southern California while also studying theater arts.