Madonna also posted a photo of herself with the caption "Don't F**k with Me", and another video of her saying "sorry, not sorry".
The result has been a showdown in the comments between the pop divas' fanbases.
The feud between the pair has been ongoing since about 2012 when Madonna publicly said Gaga "references me a lot in her work" and called her track Born This Way "reductive".
The song has been compared to Madonna's hit Express Yourself, and Madonna said: "When I heard [Born This Way] on the radio β¦ I said, 'That sounds very familiar.'"
In 2016, Gaga said: "Madonna and I are very different β¦ I play a lot of instruments. I write all my own music. I spend hours a day in the studio. I'm a producer. I'm a writer. What I do is different."
However Gaga also stated in her 2017 Netflix documentary: "I still admire her, no matter what she might think of me."