The star was edged out of contention by Bruno Mars and Kendrick Lamar, who each received multiple nominations.
Jay Z leads with eight nominations, including his first ever appearance in the album of the year list for 4:44, which comes 21 years after his debut.
Sheeran did receive several nominations in the pop categories, however.
Shape of You is up for best pop solo performance, while รท is shortlisted for best pop album.
Lady Gaga is also relegated to the pop categories for her recent album, Joanne, while Katy Perry fails to receive any nominations at all.
