Menstrual blood is one of the natural ways a woman bleeds. It is a healthy blood which comes to every women after she reaches puberty. She should not be disturbed by it nor should she be saddened by the fact that she is prevented from performing certain acts of worship because of it, since this is a command from God, the Great. However, it is a woman's responsibility to know the Sharia's rulings concerning menstruation and to worship God according to these rulings.
While they were performing the Hajj, the Prophet (peace be upon him) came to Aisha (may God be pleased with her) and found her crying. He said to her, "What is making you cry? Have you gotten your period?" She said, "Yes." So he said, "This is something God has written for the daughters of Adam. Perform all the rites of pilgrimage except circumambulation of the House (kaaba)."
This hadith (saying of the Prophet) shows that there are regulations concerning menstruation to which a woman should adhere in her worship. This does not degrade a woman, nor should she be sad on its account. As for a menstruating woman reading the Quran, scholars have disagreed on the matter. If she reads with her eyes or contemplates it with her heart without pronouncing anything with her tongue, then there is no harm in it. However, most scholars are against the permissibility of reading it out loud. They base their judgment on some weak ahadith (sayings of the Prophet).
Some scholars have gone so far as to say that there is nothing wrong with a menstruating woman reading the Quran since there is no evidence to support preventing it. This is what al-Bukhari has said. Sheikh of Islam Ibn Taymiyya says, "There is nothing in the Quran or Sunna to prevent it. The Prophetic hadith, "The menstruating woman should not read anything from the Quran" is a weak hadith. Women were menstruating during the time of the Prophet (peace be upon him). If reading [the Quran] had been forbidden to them, the way prayer is, the Prophet (peace be upon him) would have made it clear to his community and taught it to the Mothers of the Believers (the wives of the Prophet). That was simply something people spread amongst themselves. Whatever is not based on the Prophet (peace be upon him) is not reliable. Nothing to contradict the knowledge that it is not forbidden has been passed down from the Prophet (peace be upon him).
What needs to be said, after we have presented the scholarly disagreements on this matter, is 1) The menstruating woman should not read the Quran out loud unless there is a need for it: for example, if she is learning and needs to perfect her learning, or if she is being examined, and she needs to recite it for the examination, or if she is saddened daily by the fear that she may forget what she has memorized from the Quran. Then she may touch the Quran and recite it.
That is for recitation. As for dhikr (verbally remembering God) or reading the Hadith (sayings of the Prophet) and fiqh (Islamic jurisprudence), saying prayers, and listening to the Quran, nothing of these is forbidden.
As regards a menstruating woman entering a mosque, there is disagreement on this as well, but the majority of scholars are of the opinion that it is forbidden except in cases of dire necessity. And God the Highest knows best.
[This response was provided by Sheikh Saad Fadhil of the Ikhwan.]