The dog, named Dolly by those who found her, was discovered in a tent during the massive clean up operation following the event in Somerset.
Dolly was taken to nearby Happy Landings animal shelter where she was treated for a serious ear infection. Vets described her as a "sweet-natured older lady.”
Dolly Parton- who played at the festival on the Sunday- made a video message for those who found the dog, telling them she was “very honoured and flattered” that the white Lurcher had been named after her.
She said in the message: "I had my manager call the Happy Landings animal shelter to make sure the dog is being treated and cared for properly.”
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"At this time, nobody has claimed the dog and the dog is in great hands at the shelter. I will take the dog home to America if nobody claims her within a reasonable amount of time."
The animal shelter has received numerous phone calls from worried animal lovers, but so far her owner has not come forward to claim her.
Dolly said on Radio 1 following her Glastonbury slot: "I was a little bit nervous, I guess more excitement than nerves, but it was really a fun show and the people were great and I'm so happy I finally got to do it.”