Karima Rahim Massud died as the result of problems with the anasthaesia in the Nile Delta village of Gharbiya. Her death was discovered after her father sought a death certificate from another doctor.
The medical practice where the operation took place has been closed, and the doctor is being interrogated, the newspaper said.
Female genital mutilation, also known as female circumcision, is a practice that dates back to pharaonic times in Egypt. It is common in a band that stretches from Senegal in West Africa to Somalia on the east coast, and from Egypt in the north to Tanzania in the south.
The practice, which affects both Muslim and Christian women in Egypt, was banned in 1997 but doctors were allowed to operate "in exceptional cases."
Female circumcision can cause death through haemorraging and later complications during childbirth. It also carries risks of infection, urinary tract problems and mental trauma.
In June, following the death of 12-year-old Bedur Ahmed Shaker, Health Minister Hatem al-Gabali issued a decree banning every doctor and member of the medical profession from performing the procedure.
The ban must still be translated into law and could face a tough debate in parliament, but is likely to be passed.
A government survey in 2000 said the practice was carried out on 97 percent of the country's women aged between 15 and 45 years of age.
Religious leaders, usually silent on taboos relating to female sexuality, have also started to speak out against the practice, which many Egyptians believe is a duty under Islam and Christianity.
After the death of Shaker, chief mufti Ali Gomaa declared female circumcision forbidden under Islam.
Mohammed Sayyed Tantawi, the sheikh of Al-Azhar university, the top Sunni Muslim authority, and Coptic Patriarch Chenouda III also declared it had "no foundation in the religious texts" of either Islam or Christianity.