The unreleased track also makes crude references to Kylie's sister Kendall Jenner and model Gigi Hadid.
Drake took to Instagram on Wednesday to clarify that it was an old song from three years ago, and stated that he "didn't mean to offend his friends".
"A song that Mark ran last night on night owl sound live set shouldn't have been played. It's a song that leaked 3 years ago and got scrapped shortly after. He was going too keep in the drake/future catalog," Drake wrote on Instagram.
"Last thing I would want to do is wake up having any friends of mine feeling disrespected so I just had to say that to start off the day."
Last year following her split from boyfriend Travis Scott - the father of her two-year-old daughter Stormi - Kylie and Drake were romantically linked after she attended his 33rd birthday.