Does the menstruating woman perform the prostration of recitation?
Short answer
Yes, according to what the Shaykh determined; because the prostration of recitation is not a prayer in his view and purity is not a condition for it.
Evidence and explanation
The Shaykh made clear that the prostration of recitation is of the nature of remembrance and wudu' is not a condition for it in the more correct of the two views according to him.
Scholar referenced
This editorial summary is based on the original source linked below and is not presented as a verbatim quotation from the scholar.
From the text of the answer (Arabic, with an English translation)
Original answer — Shaykh ‘Abd al-‘Aziz ibn Baz
حكم سجود التلاوة للحائض والنفساء — فتوى ٩٨٠٤- Question
«هل يجوز للمرأة أن تسجد إذا مرت بآية فيها سجدة وهي في عذرها الشهري، أو من غير وضوء؟»
English translation (unreviewed): May a woman prostrate if she passes a verse of prostration while in her monthly period, or without wudu'?
- From the text of the answer
«نعم، سجود التلاوة لا يجب له الوضوء، سجود التلاوة من جنس الذكر، يجوز أن يسجد الإنسان وهو على غير طهارة، هذا هو الصواب، فإذا قرأت الحائض القرآن؛ سجدت للتلاوة، إذا مرت بسجود التلاوة، وهكذا المحدث إذا قرأ وهو على غير طهارة، لكن ليس بجنب، فإنه إذا مر بالسجدة يسجد، أما الجنب لا، لا يقرأ، نعم.»
English translation (unreviewed): Yes, the prostration of recitation does not require wudu'. The prostration of recitation is of the nature of remembrance; a person may prostrate while not in purity. This is the correct view. So if the menstruating woman recites the Qur'an, she prostrates for recitation if she passes a prostration; and likewise the one in minor ritual impurity if he recites while not in purity but not junub, if he passes the prostration he prostrates. As for the junub, no, he does not recite. Yes.
The Arabic excerpts matched the original page word for word by an automated check and have not had human scholarly review. The English translations are unreviewed translations made for this site; they are not an approved Shari‘ah translation. Rely on the Arabic original.
Source
Ruling on the prostration of recitation for the menstruating woman and the woman in post-natal bleeding
Title of the original page (Arabic): حكم سجود التلاوة للحائض والنفساء
Shaykh ‘Abd al-‘Aziz ibn Baz, may Allah have mercy on him