But it said that the incident did not signal a major change in the spread of the disease.
The WHO made its announcement at the end of a three-day bird flu conference in the Indonesian capital, Jakarta.
The case of seven family members who died from bird flu has drawn attention to Indonesia's growing problem.
Ending the closed-door conference, the WHO said its investigation suggested the virus had been passed between the family members in Sumatra.
The WHO also found that the virus had mutated in one case, but not in a way that made it more easily transmissable between people. Nevertheless, according to both the WHO and Indonesian government, the virus is widespread among poultry in the country and the focus should now be on implementing Indonesia's national strategy to contain bird flu.
To do that, they said, the country would need funding.
Indonesia has asked for $900m (�495m) over the next three years to tackle the virus.
Thirty-nine people are now known to have died from the disease in Indonesia.
The virus cannot yet pass easily from one person to another. But experts fear it could mutate and in its new form trigger a flu pandemic, potentially putting millions of human lives at risk