Praise be to Allaah.
It is permissible for a
person to delegate someone to distribute his zakaah to the needy, on
condition that the person appointed is honest and trustworthy and will give
the zakaah to those who are entitled to it. There is no differentiation in
this regard between men and women, so it is permissible to give zakaah money
to a trustworthy woman who can give it to those who are entitled to it.
The basic principle
concerning that is that it is stipulated that the appointed person be one of
those who is allowed (in sharee’ah) to handle for himself the matter that is
entrusted to him. A woman may distribute her own zakaah, so it is
permissible for her to be appointed to do that on behalf of someone else.
Ibn Qudaamah (may Allaah
have mercy on him) said: If a person is permitted (in sharee’ah) to handle
anything on his own behalf and it is something in which another person may
be appointed as a proxy, it is valid for that person to be appointed to do
that thing on behalf of others, whether that person is a man or a woman,
free or slave, Muslim or kaafir. End quote from al-Mughni (5/51).
See also Nihaayat al-Muhtaaj (5/18).
And Allaah knows best.