Police spokesman Christoph Pölzl said that the bodies of a 77-year-old man and his 76-year-old wife were found early on Monday morning in an apartment in Thomas-Morus-Gasse, and a gun was discovered lying near to their bodies.
Neighbours had become worried about the couple and called police. Police gained access to the couple's apartment through a window, with the help of a fire brigade.
Pölzl said that the body of a dog, who had also been shot, was found in the couple's apartment.
"Due to the way we found the bodies we believe we are dealing with a case of murder-suicide,” Pölzl said. The 77-year-old man had a license for the gun, which police think was used in the shootings. A suicide note has not been found.
Last week the bodies of an elderly woman and her daughter were found in the Simmering district, in another suspected case of murder-suicide.