Emma Sadler, 28, started the blaze in an under-stairs cupboard at the house in Llanrumney, Cardiff, she shared with her 59-year-old father Robert.
Cardiff Crown Court sentenced Ms Sadler to a hospital order under the Mental Health Act after she denied one charge of manslaughter by reason of insanity.
She said she was "close" to her father.
Ms Sadler, who watched proceedings via video-link from the hospital unit where she is receiving psychiatric treatment, was accused of starting the fire in January 2016 which also killed the family dog.
The court heard Ms Sadler had been showing increasing signs of mental illness and, in the days before the fire, had been exhibiting "odd behaviour".
The fire ripped through the rented house, killing Mr Sadler - who was found lying on the floor of the upstairs bathroom fully clothed.
Peter Rouch QC, prosecuting, said: "Emma Sadler deliberately and intentionally started a fire in the small cupboard under the stairs.
"The fire she started took hold and filled the house with smoke. Emma Sadler made good her escape from the smoke-filled house.
"Her father did not and he died from smoke inhalation."
Det Insp Stuart Wales of South Wales Police said: "This has been a very heartrending case.
"I want to pay tribute to the family of Mr Sadler who have shown strength and fortitude. This was a tragic incident which brought shock and sadness to the community."
A mentally ill woman who killed her father in a house fire has been found not guilty of manslaughter by reason of insanity.