Answer
Wa `alaykum As-Salamu wa Rahmatullahi wa Barakatuh.
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
In this fatwa:
1- Should there be dire necessity for you to do so, you are definitely allowed to read the Qur’an, either from your heart or mind, or by holding the Qur’an itself.
2- If there is no such necessity, then you can definitely listen to the Qur’an, for there is absolutely no evidence whatsoever in the sources to indicate that listening to the Qur’an in the state of menstruation is forbidden.
In his response to your question, Sheikh Ahmad Kutty, a senior lecturer and Islamic scholar at the Islamic Institute of Toronto, Ontario, Canada, states:
Scholars and jurists of Islam have been divided in their opinion about the issue whether women who are menstruating are allowed to read the Qur’an or not.
The generally accepted view among them is that women are not allowed to read the Qur’an while menstruating. Among other things, they have based this ruling on a report attributed to the Prophet (peace and blessings be upon him) which states, “Neither those who are sexually defiled nor those who are menstruating shall read the Qur’an.” (Ibn Majah)
A group of scholars belonging to Maliki, Shafi`i and Hanbali schools, and others, however, have rejected the above position. As has been pointed out by Imam Ibn Taymiyyah, there is nothing wrong for women to read the Qur’an either from their memory or from the mushaf itself, should they find it necessary to do so.
Even some of those scholars who are generally in favor of disallowing menstruating women from reading the Qur’an from the mushaf have considered it permissible for them to do so if they are teachers or students or they are afraid of forgetting what they have memorized.
Having cited the various views let me conclude by saying:
Should there be dire necessity for you to do so, you are definitely allowed to read the Qur’an, either from your heart or mind, or by holding the Qur’an itself. If there is no such necessity, then you can definitely listen to the Qur’an, for there is absolutely no evidence whatsoever in the sources to indicate that listening to the Qur’an in the state of menstruation is forbidden.
Therefore, you may listen to a recorded Qur’an without any inhibition; you may also read the du`aa’s (supplications) from the Qur’an at all times without incurring any sin whatsoever.
Allah Almighty knows best.
Excerpted, with slight modifications, from: www.muslims.ca