Is it permissible for a menstruating woman to recite the Qur`an from the computer without actually touching the Mus-haf?
The majority of Muslim scholars and jurists maintain the impermissibility for a woman in her menstrual period or in postpartum to recite the Qur`an or to touch the Mus-haf (copy of the Qur`an). It is the recitation itself that is prohibited regardless of the means. Therefore, it is permissible for her to read from the Mus-haf without touching it or to recall it in her head without uttering the words. There is no harm if she looks at the Qur`anic verses on the computer screen without uttering the words.
The Maliki scholars however, maintained the permissibility for a woman in her menstrual period to recite the Quran regardless of the reason of recitation (her fear of forgetting the Quran for example). And once the menstrual period ceases she is not permitted to recite the Quran until she takes a purificatory bath.
As for touching a copy of the Quran during the menstrual period, though the majority of the Muslim scholars disallow it, the Maliki scholars maintain its permissibility in case of a woman who learns or teaches the Quran.