The 30-year-old singer - whose real name is Abel Tesfaye - won Best Urban Contemporary Album for Beauty Behind the Madness in 2016, while claiming Best R&B Performance for Earned It the same year.
Then, in 2017, his third record Starboy saw him win the Grammy for Best Urban Contemporary Album again.
Back in November, he hit out after the nominees for this year's ceremony were unveiled.
He wrote on social media: "The Grammys remain corrupt. You owe me, my fans and the industry transparency ..."
The Grammys have since responded and insisted they are "surprised" he wasn't recognised and blamed the lack of nominations on there being "fewer" to hand out "than the number of deserving artists".
Recording Academy Chair Harvey Mason Jr issued a statement to Rolling Stone magazine, in which he said: "We understand that The Weeknd is disappointed at not being nominated. I was surprised and can empathise with what he's feeling.
"His music this year was excellent, and his contributions to the music community and broader world are worthy of everyone's admiration.
"Unfortunately, every year, there are fewer nominations than the number of deserving artists.
"All Grammy nominees are recognised by the voting body for their excellence, and we congratulate them all."