All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
The scholars differed in opinion on the issue of a woman handling the Quran during her menstrual period. The known viewpoint of the Shaafi’i, Hanbali and Hanafi Schools of jurisprudence is that, it is prohibited. This is the view of the majority of the scholars. This view is taken from the Hadeeth of the Prophet who said: “A woman in menses and a person (whether a man or a woman) in major impurity should not recite any part of the Quran”. However, the Maaliki School permitted the recitation of the Quran without holding it during menses. But when the menses stop, a woman should not recite the Quran before performing Ghusl. The scholars unanimously agree that she may recite with her heart only and she may look to the Quran and read with her eyes only, but she should not move her tongue. As for the touching, she should not touch the Mushaf (the Arabic text of the Quran) directly. Allaah Says (what means): {Indeed, it is a noble Quran. In a Register well-protected. None touch it except the purified [i.e. the angels]. [It is] a revelation from the Lord of the worlds.} [Quran 56:77-80]
Moreover, it was narrated in a Hadeeth that the Prophet wrote to the people of Yemen a letter and ordered them that no one should touch the Quran other than a pure person. Nonetheless, the Maaliki School permitted this for the teacher and the learner.
Allaah knows best.