Sanyal was born in 1961 to Indian Navy officer, Gulab Mohanlal Hiranandani, and his wife, Banu Hiranandani; a Sindhi family who migrated from Sindh to India at the time of the Partition of India. Her father was the mastermind of Operation Trident, the crippling Naval attack on Karachi, Pakistan during the Indo-Pakistani War of 1971.