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. We ask Allaah to exalt his mention as well as that of his family and all his companions.
We have already issued Fatwa 88368 clarifying the eight kinds of people who are eligible for Zakat. Therefore, if the housemaid whom you mentioned in the question is included in the categories of people who are eligible, like if she is poor and can't find any means to fulfil her needs, or that she is needy but could fulfil some of her needs only and not all of them, or that she is indebted and the like, then it is permissible to give her Zakat money, otherwise no.
However, we are not able to know her condition as we are unable to give a ruling about the money which she has, and whether or not it is enough to fulfil her needs and those whom she is obliged to spend on. If this is the case, then she is not among the people who are eligible for Zakat. If the money she owns is not enough for her and those whom she is obliged to support, then in this case she is eligible for Zakat. Therefore, you know more about her, however, in most cases, the housemaids are poor and needy and do not have enough money to fulfil their needs.