Hazrat Ayesha (May Allah be pleased with her) reports that the Prophet of Allah (Peace be upon Him) commanded us to perform qaza for the fasts (missed due to menstruation) after attaining purity (the end of the menstrual cycle), and he did not command us to perform qaza for the prayers (missed due to menstruation) (Tirmidhi)
In light of this hadith, it is not permissible for women to fast during their menstrual cycle, and it is obligatory for them to perform qaza for the fasts missed during this period.
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دلائل:
سنن الترمذی: (باب ما جاء فی قضاء الحائض الصيام دون الصلاة، رقم الحدیث: 787)
عَنْ عَائِشَةَ، قَالَتْ: كُنَّا نَحِيضُ عَلَى عَهْدِ رَسُولِ اللَّهِ صَلَّى اللَّهُ عَلَيْهِ وَسَلَّمَ ثُمَّ نَطْهُرُ فَيَأْمُرُنَا بِقَضَاءِ الصِّيَامِ وَلَا يَأْمُرُنَا بِقَضَاءِ الصَّلَاةِ.
الفتاوی الھندیۃ: (کتاب الحیض، 38/1، ط: رشیدیہ)
(منھا) … ان یسقط عن الحائض والنفساء الصلاۃ فلاتقضی ھکذا فی الکفایۃ … (ومنھا) ان یحرم علیھما الصوم فتقضیانہ ھکذا فی الکفایۃ۔
Allah the Almighty knows best.
Darul ifta Al-Ikhlas, Karachi.