The decision to stop the concerts came after two suspected extremists were arrested for planning an Islamist attack in the Vienna region of Austria.
According to the police, there are suspicions that a target for the attacks would be Taylor Swift's concerts later in the week, Austrian authorities report.
Austria's Federal Chancellor Karl Nehammer describes the threat as "very serious" but notes that a deed has been prevented by discovering the plans at an early stage.
"With confirmation from government officials of a planned terrorist attack on the Ernst Happel Arena, we have no other choice but to cancel the three planned concerts for everyone's safety", writes the organizer Barracuda music.
The organizer adds that all those who would attend the concert will get their tickets refunded. Approximately 65,000 spectators were expected at each show on Thursday, Friday, and Saturday.
The main suspect, a 19-year-old man, was arrested in a town south of Vienna, while the second person was arrested in the capital.
The authorities report that they have taken part in "preparatory measures" for a possible attack and that the main suspect focused on Swift's concerts. Chemical substances have been seized in the 19-year-old's home and are now being investigated.
The 19-year-old and the second suspect are believed to have been radicalized on the internet.
Taylor Swift came to Sweden for the first time in May and held three concerts in Stockholm.
