Samples from the 43-year-old woman, a resident of the island's main city Denpasar, have been sent to Jakarta for testing, said Putu Andrika, head of the bird flu control unit at Sanglah general hospital.
Two tests must come back positive for the H5N1 virus before a victim is confirmed as part of the official bird flu death toll in Indonesia, which is the highest in the world at 84.
The woman, who died on Saturday, was suffering from serious lung infection, one of the main symptoms of avian influenza, he said.
Andrika said the woman was not known to have been in contact with dead birds. Transmission usually occurs directly from birds to humans.
If confirmed to be infected with the H5N1 strain of the virus, the woman would be the third fatality on the island this month.
The deaths have raised fears of a possible negative impact on tourism here.
Thousands of birds have been culled since then as a precautionary measure and poultry has been banned from being transported in or out of the district for one month.
Both victims lived northwest of Denpasar and worked in the chicken trade.
Avian influenza was found in poultry on Bali more than a year ago.
H5N1 is endemic in birds across nearly all of Indonesia.
Scientists worry that the virus will eventually mutate into a form that is much more easily transmissible between humans, triggering a disastrous global pandemic.