Fourteen-year-old Shanjin Abdel Qader died on January 17 in a Kurdish area near the border with Turkey and Iran after contracting a severe lung infection.
Health minister Abdel Mutalib Mohammed Ali said she had contracted H5N1, despite initial reports from a World Health Organisation laboratory in Amman saying her test results for the virus were negative.
Her hometown of Ranya is just north of a reservoir that is a stopover for migratory birds from Turkey.
Her uncle, who lived in the same home, died on January 27 after suffering a pulmonary infection and samples from him were still being tested in Amman.
Iraq has called on the World Health Organisation to check the possible spread of avian flu in the country's Kurdish region where 12 people have been quarantined and bird culling is underway.
"We call on the World Health Organisation to send experts to confirm that Kurdistan is free of bird flu," said Imad Ahmed, deputy prime minister of Sulaimaniyah in Kurdish northern Iraq.
Mr Ahmed said 12 people had been quarantined after they fell ill with pneumonia, but it was feared they could possibly be infected with the fatal H5N1 strain of bird flu which has killed at least 80 people worldwide since 2003.
Iraq's Kurdish provinces, which lie on the border with Turkey, are a major poultry producing region supplying chicken and eggs for much of the entire country.
Another suspected case is 54-year-old Mariam Qadar, who hails from the same region as the two fatalities and was taken to hospital in Sulaimaniyah on Wednesday.
"The analysis so far has not confirmed if she has the disease, but there is a suspicion," hospital director Shirku Abdallah told news agency AFP.
’Don’t panic’
The health minister headed to Kurdistan on Monday amid growing fears about the spread of the lethal form of avian flu from across the border in infected Turkey.
"We are calling on Iraqis not to panic or listen to rumours, but at the same to inform us if they suspect anything," he said on Iraqi television. "Since the first cases were reported up in Turkey we have been taking all the necessary measures to deal with any possible influenza."
But the minister warned Iraqis "not to approach domestic birds and poultry as this is the main way of spreading the disease".
The government of Sulaimaniyah, run by the Patriotic Union of Kurdistan, has decided to slaughter all poultry and birds in an area near the Turkish and Iranian borders.
"Today we started a campaign to kill birds in three towns - Ranya, Dukan and Qaladaza. We formed committees to do so," said Kurdistan Health Minister Mohammed Khoshnow
The area, which consists of some 50 settlements, is not a major poultry producing region, and residents will be offered compensation.
Turkey, which has 21 cases of the flu, had previously been the only country outside Asia to report fatalities from the virus. Four children have died there.
Health officials in Iraq's three Kurdish provinces say a number of measures are being taken to stop the spread of the virus. These include decontaminating trucks crossing the border, banning the import of Turkish poultry and prohibiting the sale of live chickens inside Kurdistan.
Scientists fear that the more the virus spreads, the greater the chance H5N1 will mutate into a form that is easily transmissible between humans and spark a global pandemic that could claim millions of lives.