All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
The Prophet said: "A people who appoint a woman as their leader will never succeed." [Al-Bukhari]. This narration means that it is not permissible for a woman to lead positions of great responsibility, like being a Muslim ruler, a minister, or a judge and the like, as this leads her to mix and be in seclusion with men, and bear great responsibilities which does not befit the nature of a woman.
As regards the small positions which a woman can efficiently run and bear, and in which her responsibility is limited, then it is permissible for her to hold these positions, like running a hospital or a school. For instance 'Umar appointed Ash-Shifaa' bint 'Abdullaah Al-'Adawiyyah as an accountant for Al-Madeenah market. Ibn Hajar reported this in a biography about Ash-Shifaa' and 'Aa'ishah was appointed to take care of orphans.Allaah Knows best.