The corpses were discovered in the family's home in Boeheimkirchen, a town 55 kilometres (34 miles) west of Vienna.
"The alert was raised by the employer of one of the victims, because the person had not gone to work for some time," said Michaela Schnell, a spokeswoman for the prosecutor's office.
When they died is not known but investigators' initial findings suggest the mother shot all five members of her family before turning the gun on herself.
The dead were a 35-year-old woman, her three children -- two 10-year-old twins and a seven-year-old -- and her 40-year-old brother and 60-year-old mother.
Local media reported that the family moved into the house in 2015 and largely lived in isolation and said the children had not been in school for three days.
Austrian police stands outside a house near Boeheimkirchen, Lower Austria. Source: EPA
