In Islamic Law, the woman is like the man unless otherwise stipulated, such as is the case for some aspects of worship and in some transactions. For instance, she does not pray or fast during her menstrual period. She has to wear hijâb. She is different in giving testimony and her share in inheritance is generally less than that of a man. Except in cases such as these, all the commands of the Qur’ân and Sunnah apply equally to both sexes.
There is no evidence prohibiting a woman from being appointed as a manager, supervisor, or headmistress in some kind of work where men will be working under her direction.
Some people might try to argue this point citing the verses: “Men are the protectors and maintainers of women because Allah has given the one more (strength) than the other, and because they support them from their means” [Sûrah al-Nisâ’: 34] and “But men have a degree over them” [Sûrah al-Baqarah: 228]. However, these people must the know that this refers only to the relationship between husband and wife. The man must protect and maintain his family.
It is true that the man has a degree over the woman, but that does not mean that every man is better than every woman. A woman could be better than several men and vice versa.
Moreover, what is mentioned in the hadîth that the Prophet (peace be upon him) said: “A people who give political authority to a woman will never succeed” is only talking about high political office. Therefore, what is forbidden for a woman is to be a president or a sovereign queen. This is what was decreed by the scholars from the context of the hadîth. The Prophet (peace be upon him) made this statement when he was informed that the king of Persia had died and the Persians had appointed his daughter as their new ruler.
Therefore, if this woman is the most educated and capable among the school’s staff of males and females, then it is permissible to appoint her, provided that she observes proper hijâb and instructs the other women to do so. She has to lower her gaze from men and refrain from being alone with any of them whether in the workplace or outside of it.
And Allah knows best.