Hariadi Wibisono said the results on the 25-year-old woman, who died earlier this week, made her Indonesia's eighth confirmed death from the H5N1 strain of bird flu.
That would raise the number of deaths from H5N1 avian influenza to 69, out of 133 people known to have been infected.
"We got the result this morning. She was positive," said Wibisono, who heads a department charged with eradicating animal-borne diseases.
Officials said previously the woman had contact with dead chickens before being admitted to a Jakarta hospital. Most human bird flu cases in Asia have been blamed on direct or indirect contact with infected chickens.
Five other people have been confirmed to have contracted the virus in Indonesia but have survived.
The highly pathogenic H5N1 strain is endemic in poultry in parts of Asia.
Experts fear H5N1 could mutate into a form that passes easily among people, like seasonal influenza. If it does, millions could die.
(Additional reporting by Maggie Fox in Washington)