The victim appears to have been strangled. Her husband has been arrested, and reportedly had superficial stab wounds and cuts.
The woman’s three young children and her mother were also found in the apartment.
"There has been a homicide. The cause of death and the sequence of events is unclear," police spokesman Rainer Dionisio told the Austrian Press Agency.
The 33-year-old man contacted the police and confessed to the crime, which is thought to have occurred several hours previously.
It is not known if the children – who are reported to be one, two, and four years old – witnessed the murder. Their grandmother is said to be in shock, and all four are being cared for by the Red Cross.