Iraqi and UN health officials said Shangen Abdul Qader, a 15-year-old girl, who died in Raniya, a northern Kurdish village, on 17 January, contracted the H5N1 strain of the disease.
It was not immediately clear how she contracted it.
Abdel Mutalib Mohammed, the Iraqi health minister, said: "We regretfully announce that the first case of bird flu has appeared in Iraq. The results show the inflection with the deadly H5N1."
World Health Organisation (WHO), officials confirmed the finding.
Health teams cordoned off areas in and around Raniya on Monday and began Iraq's first mass bird cull as the government pleaded to the WHO to help prevent a large-scale outbreak.
But there were fears they might be too late.
Health officials are investigating the death of Hamasour Mustapha, 50, Abdul Qader's uncle.
Mustapha died on Friday after showing symptoms similar to bird flu.
At least two other people have been admitted to a hospital in Sulaimaniyah, 260km northeast of Baghdad, showing similar signs. Another 30 samples from northern Iraq are also being tested for bird flu.
Talabani was briefed on bird flu
The WHO is readying an emergency team to send to Iraq to carry out epidemiological tests and inspect Iraqis exhibiting bird flu-like symptoms.
Jalal Talabani, Iraq's president, met members of an Iraqi committee following up the bird flu outbreak and was briefed on efforts to protect Iraqis from any spread of the disease, according to Al-Iraqiya TV which aired footage of the talks.
Mustapha and his niece, Abdul Qader, who died after contracting a severe lung infection, lived in the same house in Raniya, a village about 100km south of the Turkish border and just 25km west of Iran.
Health officials do not yet know how the girl contracted the deadly virus, but just north of Raniya is a reservoir used as a stopover by migratory birds from Turkey, where at least 21 cases of H5N1 have been recorded.
The preliminary laboratory findings indicating the girl had bird flu were made by the US Navy Medical Research Unit laboratory in the Egyptian capital, Cairo.
The WHO said test samples have been sent to its reference laboratory in Britain for final confirmation, which could take from between several days to two weeks.