The girl's body was found on Saturday morning in the Döbling district of the capital Vienna, shocking the city.
She had been reported missing the previous day by a relative.
A 16-year-old neighbour of the girl's family was arrested overnight and later confessed, saying he had felt a "general rage" at the time of the crime but gave no further motive, police Col Michael Mimra told reporters.
The teenager had apparently led the girl into the bathroom in his family's flat. "She didn't notice he already a kitchen knife on him," Mimra said.
He is then thought to have launched a savage attack on the girl in the bath, stabbing her in the neck.
The lawyer for the girl's relatives Nikolaus Rast said that the fact that a suspect had been found was a relief for the family, in particular the girl's mother.
"She is feeling better, she is venturing out of the flat again now," Rast told the APA agency.