With at least one gunman still at large, Interior Minister Karl Nehammer warned people late on Monday to stay away from the centre of the city.
He said border checks were being reinforced and children would not be required to attend school on Tuesday.
Nehammer said “several” people had been killed. An official later clarified two people were dead, a civilian and a suspected attacker.
Vienna Mayor Michael Ludwig told broadcaster ORF a second civilian had died.
“We have brought several special forces units together that are now searching for the presumed terrorists,” Nehammer earlier told broadcaster ORF.
“I am therefore not limiting it to an area of Vienna because these are mobile perpetrators.”
Kurz said the army would protect sites in the capital so police could focus on anti-terror operations.
He said the attackers “were very well equipped with automatic weapons” and had “prepared professionally”.
Police said on Twitter at least one person had been killed and the injured included a police officer.
Vienna mayor Michael Ludwig told ORF 15 people were being treated in Vienna hospitals and seven were in a serious condition.
Police also said they had shot dead one of the attackers.
Nehammer said all six locations in the attack were near the street housing the central synagogue.
Jewish community leader Oskar Deutsch said on Twitter it was not clear whether the Vienna synagogue and adjoining offices had been the target and that they were closed at the time.
Rabbi Schlomo Hofmeister told London’s LBC radio he was living in the compound of the synagogue.
“Upon hearing shots, we looked down (from) the windows and saw the gunmen shooting at the guests of the various bars and pubs,” he said.
“The gunmen were running around and shooting at least 100 rounds or even more in front of our building.”
Videos circulated on social media of a gunman running down a cobblestone street shooting and shouting.
The attack happened hours before a partial lockdown due to the rising coronavirus spread, with restaurants, cafes and hotels shuttered and restrictions on movement at night.
Authorities gave no indication of the identity of the assailants or reason for the attack.
“We really can’t say anything about the background yet,” Kurz told ORF.
“Of course an anti-Semitic background cannot be ruled out.”
President Emmanuel Macron of France, which has seen two deadly knife attacks in Paris and Nice in recent weeks, issued a statement expressing shock and sorrow.
In 1981, two people were killed and 18 injured during an attack at the same Vienna synagogue.
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