A 31-year-old woman called the police at 5.20 a.m. (0320 GMT) on Saturday saying she had killed her children and wanted to kill herself, Vienna police said.
Officers went to an apartment in the city's Donaustadt district where they arrested a woman who had self-inflicted injuries.
The bodies of three children - aged nine and three years and an eight-month old - were found at the scene. The eldest girl was taken to hospital where attempts to revive her were unsuccessful.
Investigations remain ongoing while officers determine if the woman is fit to be questioned. The background to the incident is currently unknown, police said.