The "Like a Virgin" singer singled out Swift's music during a recent interview with Australia's Today show, where she spoke about her successors, the "princesses" of pop.
"It's good to have princesses," the singer said about the likes of Miley Cyrus and Katy Perry. "It means there's lots of pretty dresses around. I like Taylor Swift. I think she writes some really catchy pop songs, I can't get them out of my head."
When Swift got word of the comments, she took to her Tumblr page to tell her fans how she felt.
"Thanks now I'm dead," Swift wrote along with Madonna's quote. "#how am i supposed to deal with this #BE COOL TAYLOR STOP BEING EMBARRASSING" she added.
Swift, the only female act to have had three consecutive albums go platinum, faced a social media conundrum Tuesday, after a group dubbed Lizzard Squad hacked into her Instagram and Twitter accounts. The singer has since recovered control over her accounts and addressed the hack on Twitter.
Cause the hackers gonna hack, hack, hack, hack, hack..." Taylor Swift (@taylorswift13) January 27, 2015
The Material Girl faced a situation when some of the songs from her new album, Rebel Heart, were leaked online in December.
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"I was devastated," Madonna told Today's Richard Wilkins of the hack. "For an artist that's the ultimate violation. To have your work taken from you before you're finished."
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