A police statement said that the couple's car was missing and their house had been partially ransacked.
Relatives of the couple discovered their bodies at the house in Böckingstrasse on Thursday evening, police spokesman Paul Eidenberger told the Austria Press Agency.
Police officers found the man's body behind the house. He appeared to have died from severe head injuries, Eidenberger said. The woman's body was found in a courtyard leading to the house's entrance, with some injuries. The couple are reported to have been aged around 75.
The couple's car, a Citroen, was missing, and several rooms in the house appeared to have been ransacked, Eidenberger said. Police were examining the crime scene overnight and questioning the victim's relatives. The couple's son and daughter are being cared for by a crisis intervention team.
Eidenberger said it was not clear if the couple had been murdered during a robbery, and that investigations were continuing.