The British singer-songwriter, best known for songs like "As Tears Go By" and "This Little Bird," fell on Friday while vacationing on the island of Rhodes.
She was taken to a local hospital for surgery, which was described as "successful" in a statement on her Facebook page.
"Tomorrow, we will try to help her get up and we assess she needs to stay in hospital for about a week," said her surgeon, Alexandros Pittas.
Faithful, 67, also broke her back while on vacation last August. She spent four weeks recovering in the hospital.