"At 19:45 pm, three people were stabbed by an attacker," Vienna police said on its Twitter account.
Patrick Maierhofer, a spokesman for Vienna's police, told AFP the victims were a couple aged 67 and 56 years old while the daughter was 17.
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The attack took place on the large shopping street of Praterstrasse, near a subway stop in the Austrian capital.
Police said the unidentified knifeman was being hunted by officers, and that the motive and exact circumstances were as yet unknown.
Another knife attack shortly afterwards in the same area seriously wounded a 20-year-old Chechen, Maierhofer said, adding a male with Afghan nationality had been arrested.
Officers were investigating whether the two attacks are linked.
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