Is it due upon the mother to teach her daughter, after attaining the age of puberty, the necessity of removing the armpit hair or the pubic hair, or is this required only of the married woman?

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.

It is due on the parents to care about teaching their children the sound creed, Sharee‘ah rulings and Islamic manners they need in order to be brought up on Islamic teachings. Among those is to be told that removing the pubic hair and armpit hair is one of the characteristics of the Sunan of Fitrah (acts of natural predisposition), to which the Prophet guided us in his statement: “Five are the characteristics of Fitrah: circumcision, shaving the pubic hair, plucking the hair of the armpits, clipping the nails and cutting the mustaches short." [Al-Bukhari and Muslim on the authority of Abu Hurayrah]

This is not peculiar to the married woman only; rather, it is ordained for each Muslim person. It is part of the Sunnah to remove the armpit hair and the pubic hair, cut short the mustaches and clip the nails every time the hair and nails grow and are ready for that, provided that this is not delayed for more than forty days. It is proven that Anas said:

“We have been given a forty-day respite, and no more, to cut short the mustaches, clip the nails, pluck the hair of the armpits and shave the pubic hair.” [Muslim]

Allah Knows best.