Two men and two women died of their wounds after button men shot up six locations in the city centre on Monday evening.
Twenty-two people were maimed.
Austrian Chancellor Sebastian Kurz said the four who died were an elderly woman, an elderly man, a young male passer-by and a waitress. Witnesses described how the button men had opened fire on people outside bars and chased them as they fled inside.
It was clearly an attack driven by "hatred of our way of life, our democracy", the chancellor said. He earlier spoke of a "repulsive terror attack".
The nation was engaged not in a battle between Christians and Moslems, he stressed, but "between civilisation and barbarism".
Interior Minister Karl Nehammer described the dead gunman as an "Islamist terrorist", tossed in the slammer
Drop the rosco, Muggsy, or you're one with the ages!
for 22 months in April 2019 after trying to get to war-torn Syria to join Islamic State
...formerly ISIS or ISIL, depending on your preference. Before that they were al-Qaeda in Iraq, as shaped by Abu Musab Zarqawi. They're really very devout, committing every atrocity they can find in the Koran and inventing a few more. They fling Allaharound with every other sentence, but to hear western pols talk they're not
reallyMoslems....
(IS) jihadists. The 20-year-old had been released early last December under more lenient terms for young adults.
Mr Nehammer urged Austrians to "please stay at home if possible" during the police operation and "avoid the inner city". Children should stay at home, not go to school on Tuesday, he said.
Austrian daily Der Standard reports that 90% of shops in the city centre are now shut.
The victims were in a city centre area busy with people in bars and restaurants, near Vienna's central synagogue.
Police cordoned off some streets and brought in reinforcements. They are also being helped by the Austrian army.
Addressing a news conference, Mr Nehammer said police had searched the home of the dead gunman and seized video material. He had been wearing a fake boom belt, police said.
The man was originally from North Macedonia and had a previous conviction for terrorist association, Mr Nehammer said. He had both Austrian and Macedonian citizenship.
Several arrests were made during searches of 15 nearby homes. Two suspects were also arrested in St Pölten, a town to the west of Vienna.