Working for a non-Muslim is permissible as long as the job itself is permissible. There is no prohibition concerning working for non-Muslims itself.
As for the issue concerning woman’s working outside the house, we would like to quote the resolution made by Islamic Fiqh Academy, affiliated to the Organization of the Islamic Conference (OIC), in its 16th round in Dubai, the United Arab Emirates, April 9–14, 2005 / Safar 30–Rabi` Awwal 5, 1426, which tackled the differences that arise between spouses because of the wife’s working:
First: The Financial State of Each Spouse
Each spouse has an independent financial state. The wife has every right to have possessions and income of her own; she has the full legal capacity within the framework of the Shari`ah to dispose of her own income and property without having to take the permission of her husband.
Second: The Financial Support of the Wife
the husband is to provide for his wife’s sustenance and basic needs according to his financial income and the social norms agreed upon. This right of the wife is not to be denied at all except in case of her disobedience to him.
Third: The Woman’s Working Outside the House
1. The primary responsibility of the wife is to take care of her family in the home and bring up her children well. She may work outside the house if there arises a need for this, but there are certain conditions to be followed in this case: that her work suits her nature and the field of her specialization in accordance with the norms of the Shari`ah; that she sticks to the teachings of Islam [with regard to her clothing and behavior] ; and that she does not neglect her primary responsibility towards her family.
2. Her working outside the house and earning money does not mean that the husband is exempted from the religious obligation upon him of providing for her, unless she has disobeyed him by so working outside.
Fourth: The Wife’s Sharing in the Family Expenses
1. The woman is not legally obliged to share in the family expenses; this is an obligation that principally falls on the husband. Hence, it is not permissible for the husband to oblige her to take part in the family expenses.
2. However, it is desirable that the wife voluntarily participate in the family expenses, for this increases affection and enhances cooperation between the spouses.
3. The spouses may agree with each other on how to spend the wife’s salary.
4. If the wife’s going to work brings about additional expenses pertinent to her, it is she who is to pay these expenses from her income.
Fifth: Stipulating Work Before Marriage
1. The woman may stipulate explicitly in the marriage contract that she work outside the home after the marriage. If the husband agrees to this condition, it becomes binding upon him.
2. The husband may afterwards ask his wife to leave work if doing so will be for the benefit of the family.
3. It is not permissible from the viewpoint of the Shari`ah that the husband accepts the wife’s working conditional on her sharing in the household expenses or giving him a portion of her salary.
4. It is not also permissible for the husband to compel his wife to work outside the home.
Sixth: The Working Wife’s Becoming a Co-Owner With Her Husband
If the wife has contributed financially (with her own money or salary) to buying property with her husband or making a business project, she has the right to become a partner in the ownership of the said property or business according to the portion of money she has paid.
Seventh: Misusing One’s Rights Upon the Wife With Regard to Her Work
1. There are certain mutual marital duties and rights that should be observed by both spouses. The marital relationship is to be based upon fair treatment, solidarity, mutual support, and mercy. Abusing any of these rights and duties is considered a wrongdoing from the viewpoint of the Shari`ah.
2. Hence, it is not permissible for the husband to misuse his rights upon his wife by preventing her from going to work or demanding that she leaves it for no valid reason, especially if her leaving work in this case would cause more harm than good to the general interest of the family. Likewise, it is not permissible for the wife to continue working when doing so negatively affects the interest of her family and causes more harm than good.