A hospital nurse said: "The first thing she asked after waking up from a surgery was whether she still had her left hand".
Doctor Zdravko Roje said surgeons managed to save the woman's hand.
Last night she was in the hospital's intensive care unit and was said to be recovering well.
Yesterday the Ministry of Foreign Affairs and Trade confirmed it was aware of the case.
A spokeswoman told the Herald: "The New Zealand Embassy in Rome - accredited to Croatia - is providing consular assistance to the individual and their family".
Police have started an investigation into how the woman was hurt.
Croatian police said a British man was with the woman on the yacht and they were trying to track him down.
Police spokeswoman Marina Kraljevic Gudelj said: "We still did not manage to find him. We believe [the accident] was all just an unlucky case, but we would still like to talk to him."
The island of Hvar is a popular tourist spot. Many celebrities have holidayed on the island including Gwyneth Paltrow, Steven Spielberg and Prince Albert of Monaco.
Do you know this woman? Email: newsdesk@nzherald.co.nz
- additional reporting Vaimoana Tapaleao