Answer: The most apparent ruling—and Allah knows best—is that if a woman is on her menses and comes across a verse requiring Sujood Al-Tilawah, or if she wishes to perform Sujood Al-Shukr, it is not a condition for her to be in a state of purity. According to the strongest view held by scholars and supported by the apparent evidences, performing these prostrations does not require Wudu.
A woman does not need to be in a state of Taharah (ritual purity) or free from her menses to perform Sujood Al-Tilawah or Sujood Al-Shukr. If she is menstruating and wants to perform either of these acts, there is no harm in doing so. This is because neither Sujood Al-Tilawah nor Sujood Al-Shukr takes the same rulings as Salah, which requires ritual purity.
— Answered by Ustadh Abdulrahman Hassan
