She has an older sister, Helene Marla (born 1960), and an older brother, Santa Monica neurologist David B. Kudrow (born 1957). Kudrow was raised in a middle-class Jewish family. Her ancestors emigrated from Belarus and lived in the village of Ilya, in the Minsk area, and her great-grandmother was murdered in the Holocaust.
Kudrow attended Portola Middle School in Tarzana, California. In 1979, at the age of 16, she underwent rhinoplasty to reduce the size of her nose.
She graduated from Taft High School in Woodland Hills, Los Angeles. She received her BA in Biology from Vassar College, intending to follow in her father’s footsteps and research headaches. Kudrow worked on her father’s staff for eight years while breaking into acting, earning a research credit on his study on the comparative likelihood of left-handed individuals developing cluster headaches.