Video showing Minaj, 29, screaming and cursing at Carey, 42, made the rounds last week. The recording artists joined the singing competition series as judges this season.
"How dare this little girl! ... If I had been Mariah I would have walked over to Nicki and strangled her to death right there," Nicks, 64, told The Daily in an interview to promote her new documentary, "In Your Dreams."
"I would have killed her in front of all those people and had to go to jail for it," added the former Fleetwood Mac lead singer.
2014: The Year in Music [PHOTOS]