Her father, Alexander S., 26, told police he did not realise the shower was scalding hot when he threw his daughter Leonie inside and switched it on, and had not even realised she had been burned until the blisters started appearing hours later.
Medics however said that the burns were so severe it was impossible that the man could not have realised what had happened.
The parents, who live in Vienna's Floridsdorf district, also admitted that they had not immediately taken the child to hospital, and apparently left her crying almost non-stop for a day before finally deciding to take her for treatment.
She was immediately put in the intensive care ward at the Vienna SMZ hospital because of the severity of the burns on her back.
The father initially lied to medics that it had been an accident. But the extent of the child's injuries prompted medics to raise the alarm, and when he was later questioned by police, he admitted he had put her in the shower to "discipline her".
He also admitted he had often put the child in a cold shower to discipline her in the past, but that he had never wanted to harm her.
The hospital said that the child had been bought in for treatment two weeks ago, but that they had alerted police after her condition worsened.
An SMZ Ost hospital spokesman said: "The condition of the little girl worsened dramatically. She died as a result of massive organ failure. She was suffering from severe necrosis which was a consequence of the severe burns on her back. A substantial portion of the skin had been quite simply destroyed and as a result her organs failed together with the skin."
The father was questioned and released on police bail on the condition he did not return to the family home or have any contact with his wife and two other children while the investigation is continuing.
Social workers meanwhile say they are leaving the two young boys, a baby and a seven-year-old boy, with their 25-year-old mother after an examination showed that neither appeared to have any signs of abuse.
Social worker Herta Staffa said: "They are not seen to be at risk in her care. We will remain in contact with the mother to see whether she could imagine living with her partner again and to put in place a support network if he does return to the family."
The family was once previously investigated by the youth welfare office in 2012, but according to Staffa, everything was found to be as it should be.