The Shari'ah Does Not Forbid A Menstruating Woman From Reciting the Qur'an

Question :

On the Day of Arafah, is it permissible for a menstruating woman to recite certain invocations, even though they may contain verses of the Qur'an?

Answer:

There is no harm if women who are menstruating or experiencing post-natal bleeding reciting such written supplications during the rites of Hajj. There is also no harm in them reciting the Qur'an, according to what is correct. This is because there is no clear authentic text that would prevent them from reciting the Qur'an. Rather, what is mentioned specifically states that the person who is Junub is not to recite the Qur'an in that state, this is in the Hadith of 'Ali, may Allah be pleased with him. As for the menstruating woman and the woman experien- cing post-natal bleeding, it is mentioned in the Hadith of Ibn 'Umar which says:
"Neither the menstruating nor the Junub may recite anything from the Qur'an."

This Hadith is weak because in its chain, Ibn 'lyash from someone who lived in Al-Hijaz and he is considered weak when narrating from them.

Women from these two categories may recite from memory without touching the Mushaf, whereas a person who is Junub may not recite, neither from memory nor from the Mushaf, until after having performed Ghusl. The difference is that the Junub person doesn't have to endure a long period of time before reading the Qur'an, because all he has to do is perform Ghusl. And if water is unavailable, he can simply make Tayammum (i.e., to use clean sand or earth to purify himself), and then pray and recite. In a sense, the choice is in his hands. But the menstruating woman and the woman experiencing post-natal bleeding are helpless; their affair is with Allah Almighty, and they can only wait until this period has expired, after which they must take a shower; both menses and post-natal bleeding can take days.

For this reason, both categories of women may recite, so that they do not forget what they had memorized and so that they do not lose the blessings attached to reciting and learning the rules of the Shari'ah from the Book of Allah. If this is the case, then one can infer that such women can also read books that contain supplications from various Hadiths and verses of the Qur'an, or other such items. This is what is correct and the most authentic of the views of the scholars, may Allah have mercy upon them.

Source:
Ibn Baz
Fatawa Islamiyah, Vol. 7 Pages 45-46