In a now-deleted tweet, the "All I Wanna Do" singer took the organisation to task, writing, "Hey @RecordingAcad didya even read my album note? Greatest story ever about a girl listening to her heroes' records & dreaming of going off into the world to play music... then making a record with all of them, for cryin out loud!"
According to Variety, she also mocked the Grammys' perceived ageism with the hashtag, "#grammysforoldpeople."
Country star Brandi Carlile, who picked up three nominations on Wednesday, November 20 without putting an album out, and appears on Sheryl's record on a cover of George Harrison's "Beware of Darkness", backed her pal in a reply to her angry tweet.
"You made an absolutely once in a lifetime album and I love you," she added.
The 57-year-old is a nine-time Grammy-winner, but has not been nominated since 2009.
Another star who unexpectedly wasn't nominated for a Grammy this time around was 20-time winner Bruce Springsteen, his latest record "Western Stars" garnered no nods - despite again being acclaimed by critics on its release.