Praise be to Allah, the Lord of the World; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.
A menstruating woman can touch and read the explanation of the Qur'an since the saying of the Prophet (Sallallahu Alaihi wa Sallam) "Nobody should touch the Qur'an unless he is pure" [Malik] does not mean books of Tafseer and other books of Sharia. Also read the Fatawa: 83294 and 81639.
Allah knows best.