Nadia Abdel Hafez, a 37-year-old housewife from the oasis town of Fayoum, had been admitted to a local clinic on Monday.
After tests revealed the H5N1 virus, Abdel Hafez was transferred to a hospital in Cairo, some 70 kilometers (45 miles) to the north, where her condition was initially reported as stable.
But she died in the early hours of Friday, said the official, who spoke on condition of anonymity because he was not authorized to speak to the press.
Twenty-one people have been infected with H5N1 in Egypt so far, of which 13 have died. All but one of the fatalities have been women as it is they who tend to look after backyard poultry in Egypt. Women also tend to kill and cook the chickens and turkeys.
Since the outbreak of bird flu began last year, Egypt has been one of the worst-affected countries outside Asia, where the disease originated.
Also, Egypt experienced an increase in the death rate during the winter, which sparked fears that the virus might be mutating to a more drug resistant form.
The World Health Organization has reported that mutations have been found in two fatalities in Egypt. The virus had mutated to a form that might be resistant to Tamiflu, a drug also known as oseltamivir.
The WHO said the mutations were not drastic enough to spark a pandemic, but more mutations could prompt scientists to rethink current treatment strategies, reports AP.
Bird flu was first detected in Egypt in February 2006 and has spread to at least 19 of the country's 26 provinces. The previous fatality was a 17-year-old girl who died on Feb. 5.
The H5N1 strain has hit at least 45 countries and killed more than 167 people worldwide.