Sen died due to heart failure at her South Kolkata residence.
She was suffering from age-related ailments, her family said.
Sen is survived by daughter, academician Bishnupriya Dutt.
After graduating from Bethune College, Sen had joined Gananatya Sangstha and played the lead female role of "Nabanna".
Sen later joined the Little Theatre Group in 1953-54 which later became Peoples' Theatre Group.
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She had acted in many productions of the group, including "Barricade", "Tiner Taloyar" and "Titumir".
Sen had also starred in films such as Mrinal Sen's "Ek Adhuri Kahani" and "Ek Din Pratidin", Gautam Ghose's "Dekha" and Basu Chatterjee's "Pasand Apni Apni".
West Bengal Chief Minister Mamata Banerjee condoled Sen's death on Twitter, writing, "Saddened at the passing away of veteran theatre artiste Shobha Sen. My condolences to her family and friends."
CPI(M) leader Sujan Chakraborty tweeted, "Comrade Shobha Sen passed away. The brilliant. The Legendary. The Inspirational theatrical personality. Our condolence.