All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.
It is permissible that a menstruating woman makes supplication while other women affirm by saying 'Aameen. Even if these supplications include some Quranic verses, it is permissible for her to say them as long as they are said for supplication. The scholars held different views regarding whether it is permissible for her to recite the Quran or not. The sound opinion is that she is permitted to recite it. That is because there is no explicit authentic text under Sharee‘ah that prevents the menstruating woman from reciting the Quran. But she should recite without touching it.
Allaah Knows best.