This article by Shaykh Dr. Abul Hasan Hussain Ahmed is a short analysis and presenatation of some of the evidences on the impermissibility of touching the Qur’an whilst being in a state of major impurity (Hadath al-Akbar).
According to the Fiqh of the Hanafi Madhhab, it is not permissible for the one who is in the state of major impurity to touch the Mushaf (the actual text of the Holy Qur’an). This includes women in their menses and postpartum period.
The narration of Amr ibn Hazm:
In Imam Malik’s Muwatta it states:
Book 15: The Qur’an >> Section 1: The Order to Be In Wudu (When Touching the Qur’an)
Book 15, Number 15.1.1:
Yahya related to me from Malik from Abdullah ibn Abi Bakr ibn Hazm that in a letter that the Messenger of Allah, may Allah bless him and grant him peace sent to Amr ibn Hazm it said that no-one should touch the Qur’an unless he was pure.
Malik said, “No-one should carry the Qur’an by its strap, or on a cushion, unless he is pure. If it were permissible to do so, it would also have been permissible to carry it in its cover. This is not because there is something on the hands of the one who carries it by which the Qur’an will be soiled, but because it is disapproved of for someone to carry the Qur’an without being pure out of respect for the Qur’an, and in order to honour it.”
Malik said, “The best thing that I have heard about this is the ayat ‘None touch it except the purified.' (Sura 56 ayat 79). It ranks with the ayat in Surat Abasa (Sura 80), where Allah, the Blessed and Exalted, says, ‘No, it is a reminder, and whoever wishes will remember it. Upon honoured pages, exalted and purified, by the hands of scribes, noble and obedient.’ ”
 Aisha Bewley edn.
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 The commentators of the Qur’an have also mentioned that this refers to the Angels alone