Zoe Swicord Kazan was born in Los Angeles, California, to screenwriters Nicholas Kazan and Robin Swicord. She is the granddaughter of director Elia Kazan. She is of Greek (from her paternal grandfather), English, and German descent.
Kazan received her BA in Theater from Yale University. In the fall of 2006, she played "Sandy" opposite Cynthia Nixon in The New Group's production of "The Prime of Miss Jean Brodie". She returned to the stage in the fall of 2007 in Playwrights Horizon's production of "100 Saints You Should Know" and in the New Group's "Things We Want". She lives in Brooklyn.