Birgitte Kallestad, 24, was on holiday with friends when they found the puppy on a street, her family said in a statement.
The puppy is thought to have infected her when it bit her after they took it back to their resort.
She fell ill soon after returning to Norway, and died on Monday at the hospital where she worked.
It is the first rabies-related death in Norway for more than 200 years.
