Biswas was born in Nalbari, Assam, to Jagdish and Meera Biswas. Her mother, an early influence, was a history teacher and a pioneering figure for female theatre artistes in Assam; and she came into contact with artists like Bhupen Hazarika, Phani Sarma and Bishnuprasad Rabha early in life. She studied Political Science at Nalbari College, and later joined the National School of Drama, New Delhi. After graduating from NSD in 1984, she joined the NSD Repertory Company.
Seema Biswas acted as the heroine in Kishan Kartha's Amshini (Hindi) which entered the Indian Panorama Section of Filmotsav 1988. However the general belief is that Biswas debuted after Shekhar Kapur watched her perform in NSD Repertory Company, and offered her a role in Bandit Queen. Although she had earlier acted in Assamese cinema, this was her first big break into Hindi cinema, and she arrived with a bang.
Rooted firmly in theatre, she refuses to be typecast, and has worked in a variety of films and character roles. She has also worked in a number of Marathi, Malayalam, and Tamil films. Some of her Marathi films are Bindhast, Dhyaas Parwa, and Lalbaug-Parel.