Little was known about the presumed hacker, whose account was suspended by Twitter.
The user who threatened to release nude photos had the Twitter handle @lizzard and signed as 'lizard' in Japanese.
@lizzard, in a Twitter biography before the account was suspended, claimed - incongruously - to be affiliated at once with the Islamic State extremist group, the hactivist collective Anonymous and North Korea.
The account posted a number of tweets apparently reveling in the hack, including one that read: "Yes, I'm currently dating @taylorswift13".
The posts stayed up for a matter of minutes before they were apparently removed, but not before they had received thousands of retweets and favourites.
Swift's Instagram account was also hit by the hack, sending out similar messages before they were also taken down.
While some of Swift's fans - known as Swifties - rushed to defend the singer, others asked hackers to follow them from the official account while it was compromised.
All tweets since January 25 were deleted, including all of those apparently posted by hackers.
On Swift's official Tumblr she wrote: "My Twitter got hacked but don't worry, Twitter is deleting the hacker tweets and locking my account until they can figure out how this happened and get me new passwords.
"Never a dull moment."
The post was tagged with "hackers gonna hack hack hack hack hack" followed by the hashtags "#this is why I'm scared of technology" and "#who's paranoid".
Swift, whose 1989 was by far the best-selling US album released last year, famously pulled all of her music from Spotify as she said that the streaming service insufficiently compensated artists, charges denied by the Swedish company.
But Swift is intensively active on other parts of the internet. She is one of only four people with more than 50 million followers on Twitter. The others are US President Barack Obama and fellow pop stars Katy Perry and Justin Bieber.
- AFP with agencies