Sheeran has six nominations, while Beyonce, Lamar and Ronson have five each.
Swift's Blank Space will compete for best female video and pop video, while Bad Blood is up for best collaboration, direction, editing, visual effects, art direction and cinematography.
Fans can begin voting Tuesday.
Beyonce, Sia, Nicki Minaj and Ellie Goulding will battle Swift for best female video, while Sheeran, Lamar, Ronson, the Weeknd and Nick Jonas will compete for best male video.
Diplo, FKA twigs, Skrillex and Minaj earned three nominations each, while the Weeknd, Ariana Grande and Fetty Wap are double nominees.
Cyrus, who won video of the year last year for Wrecking Ball, dominated the 2013 VMAs when she grinded on Robin Thicke during a performance that trended heavily on social media. Cyrus wrote in an Instagram post that "MTV won't let me perform ... so I'm hosting this year's VMAs."
- AP