"Leave Me Alone" was the recipient of multiple nominations for its music video. The video won a Grammy Award in 1990 for Best Short Form Music Video at the 32nd Grammy Awards. The video also won the Cannes Gold Lion Award for Best Special Effects. The video also received six nominations at the 1989 MTV Video Music Awards for Video of the Year, Viewers' Choice, Breakthrough Video, Best Editing and Best Art Direction; the video won Best Special Effects. The video lost its six nominations to Neil Young's "This Note Is for You" ("Video of the Year"), Art of Noise ("Breakthrough Video"), Paula Abdul ("Best Editing"), and Madonna's "Express Yourself" ("Best Cinematography", "Best Art Direction") and "Like a Prayer" ("Viewers' Choice"). Erlewine described the music video as being "weirdly claustrophobic" and felt that, "not coincidentally," it was the "best video from the album."