A police official, speaking on condition of anonymity, said the body of the 25-year-old actress was found in her apartment in Mumbai's Juhu neighborhood late Monday.
Khan, whose real name was Nafisa Khan, was born in New York and grew up in London before moving to Mumbai.
Khan began her career in Mumbai's film industry in the 2007 Hindi film "Nishabd," in which she portrayed a teenager in love with her best friend's father, played by Bollywood superstar Amitabh Bachchan.
In her brief career she performed with other top Bollywood stars, including Aamir Khan and Akshay Kumar.
Khan last appeared in the 2010 comedy "Housefull," in which she played a supporting role.