One officer was injured when police tried to bring the situation under control, German daily Bild reported. Police reported no other outbursts after the game.
The number of Germany fans arrested was originally listed at 100, but police later corrected the figure. One Austrian was also taken into custody. Those arrested were accused of disturbing the peace and civil disorder.
German magazine Der Spiegel reported that police had to use tear gas and batons to face off against the rioters, who threw chairs, glasses and firecrackers at police.
The majority of the approximately 400-strong crowd had come to Vienna from Berlin, Erfurt and other eastern German cities. The police operation lasted for more than four hours, and entire streets were closed off.
"Vienna police made it clear that there is no place for riots in the city," police president Gerhard Pürstl said.
On Thursday night, clashes were also reported in the area around Schwedenplatz square, when 150 Germany fans brawled with their Austrian counterparts and caused damage to local pubs.
Citing Austrian media reports, Der Spiegel said drunken fans shouted right-wing slogans and made the Hitler salute in front of a bar. Three Germans were taken into custody.