The Kentucky-born singer was part of the Grammy award-winning duo The Judds, performing with her daughter Wynonna.
The pair had a string of hits, including Love Can Build a Bridge, and were due to be inducted to the Country Music Hall of Fame on Sunday.
But Judd's death was announced a day earlier by Wynonna and her other daughter Ashley, an actor.
In a statement, the sisters said they had lost their "beautiful mother to the disease of mental illness" and were "navigating profound grief."
No further details have been released about the cause of her death.
A host of industry voices, including singer-songwriter Carrie Underwood, have paid their respects to Judd on social media.
"Country music has lost a true legend," Mrs Underwood tweeted.
The Academy of Country Music has also said it is "deeply saddened" by the "heartbreaking news".
Actress Kristen Johnston tweeted that she remembered Judd as "lovely, warm and fun".
"The thing I remember best was how proud she was of her daughters," added Ms Johnston. "My heart breaks for her family."
Former Arkansas Governor Mike Huckabee said in a tweet that he was also "devastated" by her death.
"I loved her candour and humour," said Mr Huckabee, a former presidential nominee. "She is irreplaceable."
The Judds released six studio albums during a career spanning three decades, winning them many prestigious accolades - including five Grammys and nine Country Music Association Awards.
After Naomi was diagnosed with Hepatitis C, Wynonna began a solo career but they have occasionally reunited for performances. Earlier this year they announced a new arena tour, due to start in the autumn - their first in over a decade.