Doctors in the eastern Turkish city of Van say the girl, Hulya Kocyigit, was in intensive care for several days and on artificial respiration.
Her brother and sister succumbed to bird flu at the same hospital earlier this week, and a fourth member of the family is being treated for bird flu-like symptoms.
The family is from the remote town of Dogubeyazit, near Turkey's borders with Iran and Armenia, where many families depend on poultry breeding for their livelihoods and live close to their animals.
Turkish Health Minister Recep Akdag said Thursday that the family "lived in the same household with infected chickens, which they then consumed."
Humans can contract bird flu only if they come into contact with infected birds.
There has been no official confirmation of the strain, as samples are being analysed by a laboratory in Britain.
However the World Health Organisation on Thursday said the H5N1 strain is most likely the cause of the deaths.
If that is proven the case, the deaths would mark the westward spread of a virus that has killed more than 70 people in southeast Asia and China since late 2003, nearly 40 of them in 2005.
Authorities are closely monitoring the spread of the H5N1 virus, fearing it could mutate into a form easily passed between humans and spark a pandemic killing tens of millions.