Drummer Fergal Lawler said in a statement: “We are extremely surprised and honoured to receive this Grammy nomination. We’re sure Dolores would be delighted.”
The group released what will be their last album earlier this year, and the collection features vocals recorded by Dolores before her tragic death in January 2018 aged 46.
The remaining lineup – completed by brothers Noel and Mike Hogan – finished work on the LP with the support of her family.
Guitarist Noel added: “We wanted to finish this album for our dear friend and band mate Dolores.
“It’s a tribute to her, the band and our fans for the past thirty years. Being honoured with this Grammy nomination has made this whole process even more special.”
And the late singer’s mother Eileen has also released a statement as she says her late daughter would have been delighted with the recognition, although she admitted the news was “bittersweet”.
She said: “Dolores would be so happy with this, she put her heart and soul into her songs and music.
For us as her family it’s kind of bittersweet, we’re immensely proud yet saddened that she isn’t here to witness and enjoy this, although I feel that she is in spirit.”
The Grammy Awards – hosted by Alicia Keys – will take place on January 26, with The Cranberries nominated for best rock album alongside Bring Me The Horizon (‘amo’), Cage The Elephant (‘Social Cues’), Rival Sons (‘Feral Roots’) and I Prevail (‘Trauma’).