Is it permissible to prostrate solely for the purpose of supplication during menstruation?

Prostration (sujud (definition)) independent of prayer is not prescribed for a menstruating woman, nor for anyone else, even if it is for the purpose of supplication. This is because the fundamental principle in acts of worship is to pause and await evidence (from religious texts). Prostration outside of prayer is not legislated except for what has been explicitly mentioned in the evidence, such as the prostration of recitation (sujud al-tilawah) and the prostration of thankfulness (sujud al-shukr).