The 18-year-old Iraqi national is said to have come from the same circle as the main suspect, a 19-year-old Austrian with North Macedonian roots, according to the ministry.
More suspects will be questioned and properties searched as investigators continue to look into the plot, the ministry added.
The main suspect, who had vowed loyalty to Islamic State (IS), was planning a lethal assault among the estimated 20,000 "Swiftie" fans set to gather outside Vienna's Ernst Happel Stadium.
The U.S. popstar had planned concerts in Vienna on Thursday, Friday and Saturday. All three were cancelled late Wednesday over security concerns.
Two other Austrian youths aged 17 and 15 were detained on Wednesday over the alleged plot.
The 15-year-old has since been released and is being treated as a witness, the Kurier newspaper reported on Friday.
The Iraqi suspect is reported to have sworn allegiance to IS on Aug. 6, but it remains unclear whether he had anything to do with the planned attack, the newspaper reported.
Austrian authorities are reported to have received information about the Swift concert threat from U.S. intelligence, as Austrian law does not allow the monitoring of instant messaging apps, which the suspects had used to communicate.
Swift, whose next scheduled performance is in London next week, has not commented on the concert cancellations.
British police have said there was nothing to indicate that the Vienna plot would have any effect on the show.
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