The 13-year-old, identified as Soher Ebrahim, died on Thursday evening in a village in the Daqahliya governorate, Gulf News reports.
It adds her family have filed an official complaint, accusing the doctor who performed the operation of causing her death.
Soher’s father Mohammad told the Egyptian daily newspaper Al Masry Al Youm his daughter had been one of four girls being circumcised at the clinic at the time.
He said the family had been informed Soher died of an anaesthesia overdose, though this has not been confirmed.
He added: “If I had known the operation was going to kill her, I would never have [allowed] her to have it. The same doctor conducted a similar operation on her elder sister two years ago and villagers use this doctor because he has a remedy for everything at low prices."
Soher’s uncle told the newspaper the doctor in question had offered her family 20,000 Egyptian pounds (around GBP1,850) if they did not file a complaint against him.
Al Arabiya reports the police have ordered an autopsy and have “summoned” the doctor to determine the cause of the girl’s death.
It cites a health inspector report as attributing the cause of death to “a sharp drop in blood pressure resulting from shock trauma.”
The procedure of FGM was criminalised by the Egyptian parliament in June 2008, with those found guilty liable for fines and prison sentences of up to two years.
According to Egypt Independent, recent evidence suggests that younger generations are challenging the practice.
It quotes a 2008 Demographic and Health Survey of Egypt, which recorded that 91.1 percent of women aged 15-49 years underwent FGM, but only around 74 percent of girls aged 15-17 years, a percentage that is expected to drop to 45 percent over the next 10 years.
Compared to results from the 1995 survey, which recorded 96 percent of women aged 15-30 years having experienced FGM, "this is positive - if patient - progress".
The World Health Organisation defines FGM as including procedures that intentionally alter or cause injury to the female genital organs for non-medical reasons.
The procedure has no health benefits and can cause severe bleeding and difficulty urinating. Subsequent cysts, infections, infertility and complications in childbirth can lead to an increased risk of newborn deaths.
About 140 million girls and women worldwide are currently living with the consequences of FGM.
Young Indian girls clap for participants on International Women's Day celebrations organized in a college in Mumbai, India, Friday, March 8, 2013. (AP Photo/Rajanish Kakade)
Indian women react as they watch a play sensitizing women to sexual abuse and ways to raise their voice against it on International Women's Day, in New Delhi, India, Friday, March 8, 2013. (AP Photo/Saurabh Das)
Two women attend a boxing workshop of the Boxgirls Berlin in Berlin, Friday, March 8, 2013. The two women of the donation platform for social projects Betterplace visit the Boxgirls project to mark the International Womens Day. The Boxgirls Berlin are part of the Boxgirls International organization that supports women and girls using boxing programs as a catalyst for social change in their cities with the slogan 'Strong Girls, Save Communities' and supporting the women and girls empowerment. (AP Photo/Markus Schreiber)
Filipino protesters shout slogans as they prepare to march to the US Embassy in Manila to commemorate International Women's Day Friday Mar.8, 2013 in the Philippines. Thousands of Filipinos commemorate Women's Day with calls to stop violence against women and children. (AP Photo/Bullit Marquez)
A woman carries a child past a banner during a drumming session in downtown Johannesburg, Friday, March 8, 2013 to protest against violence against women and children. As the world marks International Women's Day, South Africans are locked in public soul-searching over the high level of murders and rapes perpetrated against women. (AP Photo/Denis Farrell)
A Lebanese man hangs a poster as part of an initiative set up by The Uprising of Women in the Arab World and supported by International Federation for Human Rights, in Beirut, Lebanon, Thursday, March 7, 2013. Posters representing Arab women holding a slogan saying "I am with the uprising of women in the Arab world because I want society to see me as a woman first before they see me as a mother, wife or daughter" which will be displayed in different Arab countries for International Women's Day. (AP Photo/Bilal Hussein)
An Indian woman performs Mallakhamb, a traditional Indian gymnastics on a rope on International Women's Day celebrations organized in a college in Mumbai, India, Friday, March 8, 2013. (AP Photo/Rajanish Kakade)
An Indian woman worker arranges bricks at a brick factory on International Women's Day on the outskirts of Jammu, India, Friday, March 8, 2013. (AP Photo/Channi Anand)
An image depicting a female North Korean soldier leading an artillery attack is projected on a large screen behind singers and the Unhasu Orchestra during a concert to mark International Women's Day in Pyongyang, North Korea, on Friday, March 8, 2013. The text at the top of the screen reads, "We are the Generals female coastal artillery troops." (AP Photo/Jon Chol Jin)
Indian martial arts students perform on International Women's Day in Hyderabad, India, Friday, March 8, 2013. (AP Photo/Mahesh Kumar A.)
Indian women laugh as they watch police coming down hard on an eve teaser as they watch a play sensitizing women to sexual abuse and ways to raise their voice against it on occasion of International Women's Day, in New Delhi, India, Friday, March 8, 2013. (AP Photo/Saurabh Das)