Kaur was born in Pilani, Rajasthan. Her father was an Indian Army officer, and she has a younger sister, Rubine, who is a Psychologist based in Bangalore. Her family lived in Patiala, and she studied at Yadavindra Public School, Patiala. In 1994, her father was abducted and killed by Kashmiri militants. Thereafter, her family moved to Delhi-suburb, Noida, where she grew up and attended Delhi Public School, Noida. Later, she studied at Shri Ram College of Commerce, Delhi University, and began working in local theatre.