Khan, 25, was found by her mother hanged in her room on Monday night. A post mortem is to be carried out to establish the cause of death, a Mumbai police official said.
But a police source said the death was not being treated as suspicious as it appeared to be suicide, although no suicide note was found.
He said police had questioned Suraj Pancholi, son of actor couple Aditya Pancholi and Zarina Wahab, to whom Khan had made her last phone call.
Khan, whose real name was Nafisa Khan, was born in New York and grew up in London. Her website said she went to New York to study acting at the Lee Strasberg's Institute.
Khan made her Bollywood debut in 2007 with Ram Gopal Varma's "Nishabd", playing the 18-year-old female lead opposite one of India's leading actors, Amitabh Bachchan, in a film loosely based on Vladimir Nabokov's classic novel "Lolita".
"Nishabd" received mixed reviews and did not do well at the Bollywood box office, but Khan went on to play supporting roles in two blockbusters, the psychological thriller "Ghajini" in 2008 and the comedy "Housefull" in 2010.
Her death has shocked the Indian film industry.
"Never ever seen a debutant actress with more spunk and more spirit than Jiah when i was directing her in Nishabd," filmmaker Varma wrote on Twitter.
"I dont know the reason what led to this but Jiah was very depressed about her career and scared for her future," he said in another tweet, adding that the actress had not worked for the past three years.
Fellow actress Dia Mirza tweeted: "RIP Nafisa (Jiah) Khan. You were too young and beautiful."