Sanjana Kapoor was born in the Kapoor family. Her paternal grandfather was Prithviraj Kapoor and her paternal uncles are Raj Kapoor and Shammi Kapoor. Her brothers Kunal Kapoor and Karan Kapoor have also acted in some films but like her they were not very successful. Her maternal grandparents, Geoffrey Kendal and Laura Kendal, were actors who toured India and Asia with their theatre group, Shakespeareana, performing Shakespeare and Shaw. The Merchant Ivory film, Shakespeare Wallah, was loosely based on the family, which starred her father and her aunt, actress Felicity Kendal. Sanjna attended the prestigious Bombay International School in Mumbai. She had a love for acting and frequented the Prithvi Theatre in Juhu.

Her career was not successful. She made her acting debut in the 1981 film 36 Chowringhee Lane which was produced by her father and starred her mother Jennifer Kendal in the lead. She played the younger version of the character her mother played. She later appeared in Utsav (1984), also produced by her father and played her first leading role in a Bollywood film titled Hero Hiralal (1988) which was however unsuccessful at the box office.

She then appeared in Mira Nair's critically acclaimed film Salaam Bombay in 1988 but has since quit acting in films, shifting her focus to theatre in the 1990s. In 1991, Sanjana played the role of the Japanese wife in the theatre Production of Akira Kurosawa's immortalised film Rashomon based on the Broadway play by Fay and Michael Kanin. She also acted in A.K. Bir's Aranyaka (1994). She manages the Prithvi Theatre in Juhu, Mumbai and runs theatre workshops for children.

She also hosted the Amul India Show on television for three and a half years.

In 2011, she announced her decision to leave Prithvi Theatre, and launch her own theatre company, Junoon in 2012, which would work with travelling groups staging plays at smaller venues across India.^[4]

Sanjana has been married twice. Her first husband was the actor and director Aditya Bhattacharya^[6] (famous for Mandi and Raakh), son of filmmaker Basu Bhattacharya and Rinki Bhattacharya, daughter of noted filmmaker Bimal Roy. The marriage did not last long, even though it happened after they had been in a relationship for several years.

Sanjana then married the tiger conservationist, Valmik Thapar, son of the politically well-connected socialites Romesh Thapar and his wife Raj Thapar. Valmik is a nephew of JNU historian Romila Thapar (sister of Romesh Thapar). Sanjana and Valmik have a son, Hamir.^[7] They live in Delhi and Sanjana travels to Mumbai as and when required for her film work, which has been notional for many years now. She is not involved in the mainstream Bollywood like her cousins.^[4]