Murphy, who starred in Clueless and 8 Mile, collapsed at home in Los Angeles and was pronounced dead in hospital.
The Reuters news agency is reporting that she died of a cardiac arrest.
A family statement said the “loss of our beloved Brittany is a terrible tragedy. She was our daughter, our wife, our love and a shining star.”
It added: “We ask you to respect our privacy at this time.”
Murphy’s father, Angelo Bertolotti, said: “She was just an absolute doll since she was born.
“Her personality was always outward. Everybody loved her – people that made movies with her, people on a cruise – they all loved her.”
Unconscious
Murphy was pronounced dead at 1004 (1804 GMT) on Sunday at a hospital near Beverly Hills.
Assistant Chief Coroner Ed Winter confirms the death of Brittany Murphy
She had been taken there after the Los Angeles Fire Department responded to a call at the Hollywood Hills home she shared with her husband, British screenwriter Simon Monjack.
She is reported to have been found unconscious in the shower.
Assistant Chief Coroner Ed Winter said the authorities were looking into her medical history.
“It appears to be natural,” he added.
The official cause of death may not be determined for some time as toxicology tests are required.
Los Angeles police have opened an investigation into the death.
Our Thoughts And Prayers Go Out To The Murphy’s