She was born to a Muslim mother Rukhsana Sultana and a Sikh father, army officer Shivinder Singh Virk, from a feudal family. Her mother was a political associate of Sanjay Gandhi during the Indian Emergency in the 1970s. Through her paternal grandmother Mohinder Kaur, Amrita is the great-granddaughter of Sobha Singh, one of the builders of New Delhi, and the great-niece of the late novelist Khushwant Singh. The actress Begum Para is her great-aunt and her husband was Nasir Khan, who is the brother of Dilip Kumar. Actor Ayub Khan is her second cousin. Singh was a childhood friend of Shahrukh Khan. Their mothers often worked together in the Old Delhi area and Singh attended the same school as Khan's sister, Shahnaz.