The ceremony, filmed at several outdoor New York locations with a limited audience, was dedicated to the late Black Panther star Chadwick Boseman.
It included pre-recorded speeches and performances, with Lady Gaga saying: "Love who you are. Be kind. Mask up."
Host Keke Palmer called Boseman, who died on Friday, "a true hero".
Gaga's wins were for best artist, song, collaboration and cinematography, plus the first MTV Tricon Award - honouring her work in music, acting and fashion.