Preliminary indications suggest that the 26-year-old man "clearly had sympathies with political Islam", Michaela Kardeis, head of public security, told a news conference in Vienna.
Material seized at his home would be further analysed in the coming days, Kardeis said, but for now there are no more details about the attacker's background or possible motives.
The man attacked the soldier outside the Iranian envoy's residence just before midnight (2300 GMT) on Sunday, stabbing him several times as they wrestled on the ground.
The soldier initially tried to use pepper spray to immobilise his attacker but later used his gun, firing at least four shots and killing the attacker at the scene, according to police.
The soldier escaped relatively unscathed, with a wound to his upper arm for which he was treated in hospital. He was also suffering from shock.
Police have ordered reinforcements around all diplomatic missions in the city.