After graduation as a Dancer from the London Contemporary Dance School, Indrani took the role of Cassandra in the original 1981 West End production of Cats by Andrew Lloyd Webber. She then undertook various pieces of stage work, including seasons at the Royal National Theatre, The Royal Exchange, and the Royal Shakespeare Company.
From October 1987 to 1989, Seeta played Anita Sharma in BBC Radio 4's drama series Citizens.
Indrani is co-founder and co-owner of MashMosh Films with Editor Chris Bishop. Created in 2004, its productions include Asians in Europe, a promo film for Asian Music Award winner DJ Swami funded by Sony Entertainment Television Asia, and short film Snapshots and full production The Good time Girls which both debuted at the Cannes Film Festival.
From October 2008 to March 2010 she appeared in the role of Dr. Lily Hassan on the BBC One daytime soap, Doctors. She portrayed Afia Khan's maternal aunt Shameem on EastEnders in 2011. In 2011, Indrani appeared as Brenda Kiely in the Sky1 comedy drama series The Cafe. In 2013, she made a guest appearance as DCI Stella Morton in the BBC One drama series Casualty in the episode "Badge of Honour". Indrani portrayed Harita in nine episodes of Catastrophe in 2015 and 2017.