The girl was from Pamulang, on the outskirts of the capital, Jakarta.
Her 10-year-old brother is also said to have died after showing flu-like symptoms, but health officials say they did not manage to obtain any samples.
The family reported that a number of chickens near their house died before the children fell sick.
Since late 2003, bird flu has killed more than 120 people worldwide, mostly in Asia.
Bird flu is passed to humans who are in proximity to poultry infected with the H5N1 strain of the virus.
Scientists warn that contact between infected birds and humans could lead to the virus mutating into a form that easily passes between humans, sparking a pandemic that could kill millions.