It is permissible for a woman to make the Adhan for the congregation of women.
Question:
If there is a group of women present at the time of prayer, can they make the Adhan (call to prayer) and the Iqamah (call to perform prayer)? Can they pray in congregation?
Answer:
All praise is due to Allah, the Lord of the Worlds, the Beneficent, the Merciful, the Master of the Day of Judgment.
There are three cases for women’s making Adhan or Iqamah:
First: If men and women are present to perform the prayer, in such case it is not valid for a woman to make Adhan or Iqamah because men are entitled to do that and her Adhan and Iqamah is not sufficient for the congregation of men.
Second: Making the Adhan and the Iqamah for the congregation of women only.
Third: Making the Adhan and the Iqamah individually just for herself.
It is permissible for a woman to make the Adhan for the congregation of women or for herself although this is not obligatory upon her like men. However, it is permissible to make the Adhan in this case but she must lower her voice.
Regarding the Iqamah for herself or the congregation of women, it is preferable. Yet, if she does not make the Iqamah, the prayer is still valid.
As for leading the prayer, there are two cases:
First: A woman leading the congregation of men or both men and women in prayer, in such case it is not valid at all whether it is obligatory or supererogatory (nafl) prayer.
Second: A woman leading women in prayer, in such case it is recommended for women to pray in congregation if they happened to be in one place. A woman among them leads the prayer, but she is to stand in the middle of the first line. A woman leading the congregation of women in prayer is correct and permissible.
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Source: translated and adapted form islamqa.info.