One of the messages told users to follow a user with the handle @Lizzard.
That user's Twitter biography claims to be a "leader of Lizard Squad", as well as a number of other famous hacking groups such as LulzSec and Anonymous. The account posted a number of tweets apparently revelling in the hack, reported Independent online.
The posts stayed up for a matter of minutes before they were apparently removed, but not before they had received thousands of re-tweets and favourites.
While some of 25-year-old 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.
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