Answered by Shaykh Faraz Rabbani
Question: Is it permitted for a menstruating woman to recite the Qur’an? What about reading a du`a that has Qur’an in it?
Answer: It is permitted to read the Qur’an without actually reciting the words or touching it (e.g. by looking at it, such as from a computer screen), though not to recite it, when menstruating. It is also permitted for women to read Qur anic verses for protection, dua, and the intention of dhikr (as opposed to Qur anic recitation), even if out loud. Therefore it is not disliked for women in their periods to recite litanies (ahzab, sing: hizb) of supplications, such as those of Imam Shadhili, Imam Haddad, Imam Nawawi, and others.
It is recommended in the Hanafi school for women in their periods to sit making dhikr in the place they normally pray, in order to keep up their good habits. It is also highly praiseworthy to listen to the Qur an, even recorded. There is great benefit if this is from the recitation of a master, such as Hussary.