The incident happened in Brüßlgasse in Ottakring when several neighbours called police after hearing noises and a woman's screams coming from a nearby flat.
“A man had gone on a rampage and damaged several objects,” police spokesman Patrick Maierhofer told Radio Wien.
As four police officers approach the third floor flat, the man - named as Ismail S. by Österreich newspaper - reportedly came out of the open apartment door holding two knives.
The officers demanded 37-year-old Ismail S. put the weapons on the floor but he refused, and instead “went at the officers with two 20 centimeter large kitchen knives”, according to Maierhofer.
“He continued running, then the shots were fired,” he said.
It was not clear from police how many officers fired their weapon nor how many shots were made, although witnesses reported hearing four shots. The man then collapsed and died in the stairwell.
The 30-year-old wife of the man was found in the apartment and taken away by the police crisis intervention team.
Second shoot-out in recent weeks
The dramatic incident follows a shoot-out between police and a supermarket robber in Vienna earlier in July that left one officer and the robber dead.
Two employees of the Billa supermarket in Hütteldorferstraße were held at gunpoint by the robber in the supermarket after it was closed.
The officer who was killed, named as Daniel S., was one of three police officers who responded to a silent alarm triggered during the armed robbery.
After escaping the supermarket, the suspect - from Bosnia - is believed to have been shot and killed by WEGA armed police unit, when they encountered him in a nearby stairwell.
An accomplice - an Austrian named Wolfgang A. - was arrested a few days later, suspected of driving the getaway vehicle. Police also found a variety of deadly weapons and munitions in his home.