Perry was also nominated for best female video for "Firework," and best pop video for "Last Friday Night (T.G.I.F)."
Also collecting a number of nominations were Adele and Kanye West, who tied at seven nominations. Adele will compete with Perry for top video with "Rolling in the Deep."
Others in the category include the Beastie Boys for "Make Some Noise"; rapper Tyler, the Creator for "Yonkers"; and Bruno Mars for "Grenade."
Mars was nominated for four Moonman trophies. Other multiple nominees include Lady Gaga, Beyonce and Eminem.
The VMAs will air live from Los Angeles on Aug. 28.
The Associated Press contributed to this report.