The rapper Nicki Minaj reacted on Tuesday to not being nominated for MTV’s coveted Video of the Year award by saying that the cultural contributions of black women are often overlooked, raising the specter of racism in the music industry, and setting off a Twitter debate that drew thousands of people — including Taylor Swift.

Ms. Minaj, whose music video for “Anaconda” held a video streaming record until it was broken by Ms. Swift’s “Bad Blood” video in May, felt that “Anaconda” and “Feeling Myself,” a collaboration with Beyoncé, should have been nominated. (Another video by Beyoncé, “7/11,” was.) Ms. Minaj did garner nods for other MTV Video Music Awards.