Khan’s mother found her body hanging at her home, police told the BBC. No suicide note has been found, they said.
A post-mortem examination is to be carried out to establish the cause of death and police say they are seeking information from her neighbours.
The 25-year-old actress made her debut in 2007 with Amitabh Bachchan. She also acted with Aamir Khan and Akshay Kumar.
“Nafisa Khan, who is known as Jiah Khan, was found hanging by her mother at around 22:45 India time [17:15GMT] ) at her residence on the first floor of Sagar Sangeet [apartment],” deputy commissioner of police Chhering Dorje said.
“Her body has been taken to the hospital where a post-mortem will be conducted to find the cause of her death,” he added.
Jiah Khan was born in New York and grew up in London before moving to Mumbai for a career in Bollywood.
She acted in Nishabd, starring Bachchan, and the psychological thriller, Ghajini, which had Aamir Khan in the lead role.
Her last film was in the 2010 comedy Housefull, in which she played a supporting role.
‘Too young to go’
Her death caused shock within the film industry.
“Never ever seen a debutant actress with more spunk and more spirit than Jiah when I was directing her in Nishabd,” filmmaker Ram Gopal Varma wrote on Twitter.
Bachchan also took to Twitter to react on his colleague’s death: “WHAT …!!! Jiah Khan? What has happened? Is this correct? Unbelievable!!!”
Wrote fellow actress Dia Mirza: “RIP Nafisa (Jiah) Khan. You were too young and beautiful…”
Filmmaker-choreographer Farah Khan tweeted: “Can’t register that Jiah is no more… Worked with her in Housefull and she was so beautiful and such a good soul. Too young to go Jiah.”
Jiah Khan’s “official” website says she was born in New York and brought up in London. It says she went to New York to study acting.
She also featured in an advert for the animal rights group, People for the Ethical Treatment of Animals
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