In Islam, the status of women is unique. Islam honors women and regards them as equal and vital to life as men. Generally speaking, in Islam, women are permitted to work provided that the work itself is lawful, the working woman abides by Islamic morals of dress, talk, etc., and the working wife avoids neglecting her main duty, which is looking after her children and husband.
Therefore, if a woman is qualified to do a certain job, then she is allowed to work.
Sheikh Ahmad Kutty, senior lecturer and Islamic scholar at the Islamic Institute of Toronto, Canada, stated: There is nothing wrong for a woman to work in a university as a lecturer, as long as she is conscientious in following the Islamic ethics while performing your duties. In fact, Islamic history is full of woman scholars who taught both men and women. Some of our great scholars, such as Imam Shafi`i, Ibn Taymiyah, and Ibn Hajar, had among their teachers woman scholars who taught them Hadith sciences. So, you need not feel any qualms about your job as a professor or a lecturer, as long as you remain true to your duties as a Muslim.