Allah authorizes child-marriage. In a surah regarding divorcing wives:
And those who no longer expect menstruation among your women - if you doubt, then their period is three months, and [also for] those who have not menstruated. And for those who are pregnant, their term is until they give birth. And whoever fears Allah - He will make for him of his matter ease.
Explained by Tafsir al-Jalalayn.
And [as for] those of your women who (read allā’ī or allā’i in both instances) no longer expect to menstruate, if you have any doubts, about their waiting period, their prescribed [waiting] period shall be three months, and [also for] those who have not yet menstruated, because of their young age, their period shall [also] be three months — both cases apply to other than those whose spouses have died; for these [latter] their period is prescribed in the verse: they shall wait by themselves for four months and ten [days] [Q. 2:234]. And those who are pregnant, their term, the conclusion of their prescribed [waiting] period if divorced or if their spouses be dead, shall be when they deliver. And whoever fears God, He will make matters ease for him, in this world and in the Hereafter.
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Narrated `Aisha:
that the Prophet (ﷺ) married her when she was six years old and he consummated his marriage when she was nine years old, and then she remained with him for nine years (i.e., till his death).
Narrated `Aisha:
that the Prophet (ﷺ) married her when she was six years old and he consummated his marriage when she was nine years old. Hisham said: I have been informed that `Aisha remained with the Prophet (ﷺ) for nine years (i.e. till his death).
Narrated Hisham's father:
Khadija died three years before the Prophet (ﷺ) departed to Medina. He stayed there for two years or so and then he married `Aisha when she was a girl of six years of age, and he consumed that marriage when she was nine years old.
Narrated `Aisha:
I used to play with the dolls in the presence of the Prophet, and my girl friends also used to play with me. When Allah's Messenger (ﷺ) used to enter (my dwelling place) they used to hide themselves, but the Prophet would call them to join and play with me. (The playing with the dolls and similar images is forbidden, but it was allowed for `Aisha at that time, as she was a little girl, not yet reached the age of puberty.) (Fath-ul-Bari page 143, Vol.13)
['A'ishah] replied, "There are nine special features in me that have not been in any woman, except for what God bestowed on Maryam bt. Imran." By God, I do not say this to exalt myself over any of my companions." "What are these?" he asked. She replied, "The angel brought down my likeness; the Messenger of God married me when I was seven; my marriage was consummated when I was nine; he married me when I was a virgin, no other man having shared me with him; inspiration came to him when he and I were in a single blanket ; I was one of the dearest people to him; a verse of the Qur'an was revealed concerning me when the community was almost destroyed; I saw Gabriel when none of his other wives saw him; and he was taken (that is, died) in his house when there was nobody with him but the angel and myself."
-- "The History of al-Tabari," Vol 7.
‘A’ishah states: We came to Medina and Abu Bakr took up quarters in al-Sunh among the Banu al-Harith b. al-Khazraj. The Messenger of God came to our house and men and women of the An$ar gathered around him. My mother came to me while I was being swung on a swing between two branches and got me down. Jumaymah, my nurse, took over and wiped my face with some water and started leading me. When I was at the door, she stopped so I could catch my breath. I was then brought (in] while the Messenger of God was sitting on a bed in our house. [My mother] made me sit on his lap and said, "These are your relatives. May God bless you with them and bless them with you!" Then the men and women got up and left. The Messenger of God consummated his marriage with me in my house when I was nine years old. Neither a camel nor a sheep was slaughtered on behalf of me.
-- "The History of al-Tabari," Vol 9.