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Riya comes from a celebrity family, as her grandmother Suchitra Sen is one of the greatest Bengali actresses of Bengali films. Her mother Moon Moon Sen was also an actress and her father is a member of a Tropura Royal family. Her paternal grandmother Ila Devi, was the princess of Cooch Behar, whose younger sister Gayatri Devi is the Maharani of Jaipur. Before moving to Mumbai, she lived with her parents and sister Raima Sen, who is also an actress, in Kolkata.
Before entering show business, she studied at Loreto House and Rani Birla College, both in Kolkata, but dropped out of both institutions. She also briefly studied at the National Institute of Fashion Technology. Since her Bollywood debut, she has moved from Kolkata to Juhu in Mumbai.