Desai was born in Philadelphia, but grew up in Binghamton, New York. Her parents are physicians; her father is Indian and her mother is Filipina. She cultivated an early interest in performance and was active in the musical and acting life of her schools. After graduating from high school in 1990, she attended and graduated from Oberlin College. In 1997, she earned her MFA at New York University in its Tisch School of the Arts Graduate Acting Program.