Is There a Set Age for Marriage in Islam?

Assalamu’alaikum warahmatullahi wabarakatuh,

IN THE NAME OF ALLAH, THE MOST BENEFICENT, THE MOST MERCIFUL

Firstly: 

Islam does not give a specific age for marriage, either for the husband or for the wife. Allah, may He be exalted, says (interpretation of the meaning):

“And for such of your women as despair of menstruation, if ye doubt, their period (of waiting) shall be three months, along with those who have it not”

[al-Talaaq 65:4]. 

Al-Sa‘di (may Allah have mercy on him) said: “along with those who have it [menses] not” means minors, those who have not yet started to menstruate. Adult women who have never menstruated at all are like those who “despair of menstruation” (i.e., have passed menopause); their ‘iddah is three months. 

Tafseer al-Sa‘di, p. 870 

The Prophet (blessings and peace of Allah be upon him) married ‘Aa’ishah (may Allah be pleased with her) when she was six years old and the marriage was consummated when she was nine years old. Narrated by al-Bukhaari (4840) and Muslim (1422). 
Ibn Qudaamah (may Allah have mercy on him) said in al-Sharh al-Kabeer, 7/386: 

With regard to females, the father may give his minor, virgin daughter who has not yet reached the age of nine in marriage, and there is no difference of opinion concerning that, if he gives her in marriage to someone who is compatible. Ibn al-Mundhir said: All of those scholars from whom we acquired knowledge unanimously agreed that it is permissible for a father to give his minor daughter in marriage if he arranges her to someone who is compatible, and it is permissible for him to do that even if she is reluctant.

Secondly: 

No one may give a minor daughter in marriage except her father according to the view of Maalik and Ahmad. This was also the view of al-Shaafa‘i, but he regarded the grandfather as being like the father in that regard. Abu Haneefah said – and it was also narrated from Ahmad – that it is permissible for a guardian other than the father to give (the minor girl) in marriage, but the more correct view is the former one.

See: al-Mughni, 7/33 

Thirdly: 

The father should not give a minor daughter in marriage except in a case where he thinks it is in her best interests. Just as he may only dispose of her wealth in that which is in her best interests, the same applies with regard to arranging her marriage. Islam only permits that to the Muslim father who is pious and pays proper attention to the best interests of his children, and who understands very well that he is a shepherd and that he is responsible for his flock. 

Ibn Wahb narrated that Maalik said, with regard to a man arranging a marriage for an orphan girl under his care: If he thinks that (the husband) is a man of virtue, righteousness and wisdom, it is permissible for him to do that. 

Ahkaam al-Qur’aan by al-Jassaas, 2/342 
Fourthly: 

A man should not consummate marriage with his young bride until she is physically able to bear intercourse. This varies from one time, place and environment to another. 

What young men and guardians of girls should do is hasten to arrange marriages, so as to guard chastity and protect honour, and so as to attain the great purposes for which Allah ordained marriage. 

Allah knows best.