The victim is the sister of a 14-year-old boy who died from bird flu on Sunday in the town of Van.
He was the first fatal case of the deadly virus outside Asia.
Doctor Ahmet Faik Oner said the girl, Fatma Kocyigit, whose age was not released, died at 6.30am after being in a critical condition since Wednesday.
"We lost Fatma Kocyigit this morning," said provincial governor Niyazi Tanilir.
He said one patient is in a serious condition and another in a less serious condition.
"Two people have therefore died of bird flu in Van," the doctor said.
Doctors at the Van hospital initially gave the cause of death for teenager Muhammed Ali Kocyigit as a lung infection linked to pneumonia.
But further tests showed that the youth, from the remote town of Dogubeyazit near Turkey's borders with Iran and Armenia, had died of avian influenza.
"Two patients (including the dead teenager) have tested positive, and there is another suspected case," Health Minister Recep Akdag said.
The suspected third case is the third of the four siblings hospitalised in Van on Saturday, the minister said.
All of them "lived in the same home along with diseased chickens and ate them," he said.
The World Health Organisation has been informed of developments and a special team from the health ministry will head for Van on Thursday, Mr Akdag told reporters.
He called on residents of Dogubeyazit and surrounding villages to avoid any contact with fowl.
Hospital sources in Van said they have interned a handful of other children with similar symptoms on Thursday, also from Dogubeyazit but not from the same family.
Dogubeyazit is about 100 kilometres south of Aralik, a village on the flight path of migratory birds blamed for the spread of the epidemic.
Aralik was put under quarantine last week after fowl there tested positive for the H5 strain of bird flu.
Officials are still awaiting the results of further tests being conducted in London to determine whether any of some 750 birds slaughtered in the village suffered from the H5N1 strain of bird flu, which can be deadly to humans.
The first case of H5N1 in Turkey was discovered in October at a turkey farm in Kiziksa, a village in the north-eastern province of Balikesir, near a wildlife reserve that is a well-known stopover for migratory birds.
Officials said on December 9 that they had eradicated the avian flu virus in the region after testing thousands of samples and culling 10,000 birds.
Experts have warned that Turkey faces a prolonged threat of bird flu outbreaks because it lies on the flight path of migrant fowl.
More than 70 people have died from bird flu in Asia since late 2003, nearly 40 of them in 2005 alone.
The latest was believed to be a 39-year-old man who died at a hospital in Jakarta on Monday, one day after he was admitted suffering from symptoms of bird flu.
Experts say the feared H5N1 virus could merge with human strains of flu to create a global outbreak that could kill millions of people around the world.