"I think we should stop allowing ourselves to be shocked every year by the disconnect between impactful music and these awards," said the star.
"This is a great time for somebody to start something new that we can build up over time and pass on to the generations to come."
The Grammys have yet to respond.
Drake was speaking after The Weeknd was overlooked in Tuesday's nominations. The star, whose album After Hours is the year's best-selling record in the US, was widely expected to feature in the album of the year and song of the year categories.
After the shortlist was revealed, the singer, whose real name is Abel Tesfaye, called the ceremony "corrupt", adding: "You owe me, my fans and the industry transparency".
In a follow-up tweet, he expressed disbelief that the organisers had asked him to perform despite the snub.
"Collaboratively planning a performance for weeks to not being invited? In my opinion zero nominations = you're not invited!"