There is a popular book called “Reliance of the Traveler” (عمدۃ السالک, cumdatu-s-saalik) which is a sort of portable shareecah. Going through it, I was a little shocked to find this:
ویجب (علی کل من الذکر والأنثی) الختان (وھو قطع الجلدۃ التي علی حشفة الذکر وأما ختان الأنثی فھو قطع البظر [ویسمی خفاضًا]).
Translation per Nuh Ha Mim Keller: Circumcision is obligatory (O: for both men and women. For men it consists of removing the prepuce from the penis, and for women, removing the prepuce (Ar. bazr) of the clitoris (n: not the clitoris itself, as some mistakenly assert). (A: Hanbalis hold that circumcision of women is not obligatory but sunna, while Hanafis consider it a mere courtesy to the husband.) (“e4.3” of the book.)
More literal translation: And it is obligatory (upon all men and women) the circumcision (and it is the cutting off the skin that is on the glans of the male and on the other hand the circumcision of the woman it is the cutting off of the clitoris [and it is considered decreasing]).
Ahmad ibn Naqib al-Misri (trans. Nuh Ha Mim Keller). Reliance of the Traveller. Delhi, India: Aamna Publishers, 1994, p. 59. If an Arabic-speaker can give a better translation for the text, I would appreciate it very much.
Circumcision is obligatory (for every male and female) by cutting off the piece of skin on the glans of the penis of the male, but circumcision of the female is by cutting out the clitoris (this is called khufaad).
“Khufaad” can be considered to mean “shortening,” “decreasing,” “diminishing.”
The Shāfi‘ī school is followed throughout the Ummah, but is most prevalent by Kurds in Kurdistan (in Turkey, Iraq, Syria, Iran) and by other communities in Egypt, Somalia, Yemen, Indonesia, Thailand, Singapore, Philippines, Sri Lanka, Palestine, Syria and is the official madhab followed by the government of Brunei Darussalam and Malaysia. It is followed by approximately 15 percent of Muslims world-wide.
The Shāfi‘ī tradition is accessible to English speakers from the translation of the Reliance of the Traveller.
So the good news is that female circumcision is not obligatory according to all four schools of jurisprudence: only the Shaaficee school of jurisprudence holds it as mandatory, which would explain why it is so prevalent in Africa and why al-Azhar supports it. The bad news, though, is that many Muslims (evidently, according to Wikipedia, 15% of Muslims) hold it as mandatory.
Update: Added another translation.