Fox News broadcaster reported that the husband of the 32-year-old actress had called emergency services for help when she fell ill.
Meanwhile, Los Angeles police were investigating the her death, and the coroner plans to carry out an autopsy, People magazine reported.
Murphy, who played in films such as Sin City, 8 Mile, Girl Interrupted, Clueless and Just Married.
Murphy, who had been acting since age two, was apparently found unconscious at her home, in her shower, on Sunday morning by her mother, the celebrity gossip website TMZ reported.
The actress was transported to Cedars-Sinai Medical Centre in Los Angeles, where she was pronounced dead, The Los Angeles Times reported.
Actor Aston Kutcher, with whom she starred in the 2003 film "Just Married", sent condolences to her family via the internet social network site Twitter and said: "The world lost a little piece of sunshine."
Murphy drew attention with her portrayal of the street-smart Tai in the teenage 1995 classic "Clueless". In 1999, she starred with Angelina Jolie and Winona Ryder in "Girl Interrupted".
Murphy's husband, screenwriter Simon Monjack, made news in November when he was rushed to hospital after a flight that landed in Los Angeles, when he had unspecified medical problems.
