During menstruation, women can read the Qur’an and make dhikr (remembrance of Allah) and du`aa (supplication), though they are forbidden from fasting, performing salah (Prayer) and touching the mushaf (copy of the Qur’an). In this way, they still have the opportunity to engage in dhikr and du`aa’ while menstruating. They can also read and touch translations of the meanings of the Qur’an.

We’d like to furnish you with the following fatwa issued by Sheikh AhmadKutty, a senior lecturer and Islamic scholar at the Islamic Institute of Toronto, Ontario, Canada , who states: “A woman is certainly allowed to engage in dhikranddu`aa while menstruating. As Imam Nawawi pointed out, there is a virtual consensus among scholars and jurists that both men and women in a state of sexual defilement (janabah) and women while menstruating or undergoing a postpartum period of bleeding can make dhikr either through spoken words or silently in their hearts.
It is also permissible for them, while making supplications, to use the familiar du`aa’s that are taken from the Qur’an such as the following:
Rabbanaa hab lanaa min azwaajinaa wa dhurriyaatinaa qurrata a`yunin wa ij`alanaa li al-mutaqeena imaman (Our Lord, grant us true joy in our spouses and children and make us role models for those who are mindful [of You]).
Rabbanaa aatinaa fi ad-dunya hasanatan wa fi al-aakhirati hasanatan wa qinaa adhaaba an-naar (Our Lord, grant us good in this world and good in the next world and save us from the torments of the Hellfire).

Rabbanaa taqabbal minnaa innaka anta as-samee`u al-`aleem wa tub `alaynaa innaka anta at-tawwaab ar-raheem (Our Lord, accept this work of ours, for verily You are All-Hearing, All-Knowing; and grant us repentance, for You are the Relenting, the Merciful).

Having clarified the above, it becomes clear that in the time of tahajjud, a woman during her period is allowed to recite the Qur’an (from her memory), make dhikr and du`aa’, and recite translations of the meanings of the Qur’an or books of Tafsir, etc.

She can supplicate Allah using any form of du`aa’ she likes. She can also make istighfar (asking Allah for forgiveness) which is something good in this time. Finally, we ask Allah Almighty to reward you and grant you happiness in this worldly life and in the Hereafter.