Reference: Fataawa ash-Shaykh al-‘Allaamah Muhammad Naasiruddeen al-Albaanee fil-Madeenah wal-Imaaraat – Page 68-70
Question: Is it permissible for a man or a woman to recite the Qur.aan or touch the mus.haf without [being in a state of] wudhoo?
Response: Reciting the Qur.aan without [being in a state of] wudhoo is permissible. This is because there is no text from the Book or the [authentic] Sunnah opposing this [viewpoint], i.e. [expressing] the impermissibility of reciting the Qur.aan without [being in a state of] wudhoo.
And there is no difference in that between the man and the woman, rather, there is no difference in that between the man who is in a state of purity and [the man who is] in a state of impurity, [just as there is no difference between] the menstruating woman and the woman who is not on her menses.
And from the evidences to support this [opinion] is the hadeeth of ‘Aa.ishah in Saheeh Muslim: The Prophet ﷺ would [engage in the] remember[ance of] Allaah in whatever state he was in.
So it has been legislated that the menstruating woman is not to pray, and her not being allowed to pray is for [some] great wisdom in that she worships Allaah Ta’aala just as she worships him before the onset of the menses.
So it is not permissible for us to restrict her circle of worship which was legislated for her when she was praying; So when she was prohibited from praying, she was not prohibited from anything else. So we must accommodate that which Allaah has [legislated] in accommodating the people.
And many a time, on such an occasion I mention the hadeeth of ‘Aa.ishah when she was performing hajj with the Prophet ﷺ, and they descended upon a place which was called Sarf – which is close to Makkah; [There] he ﷺ found her crying because of [the onset of] her menses, so he said to her:
«Do what the hajj pilgrim does, without performing the tawaaf or praying».
So he did not prevent/deny her from reciting the Qur.aan nor entering al-Masjid al-Haraam.
 Transmitted by Muslim 1/182;
 Transmitted by al-Bukhaaree 3/588.