The Zoroastrian demoness associated with menstruation is Jahi.
Jahi is an Avestan female demonic figure linked with licentiousness, sexual disorder, and ritual pollution. In later Middle Persian tradition, she is described as the consort of Ahriman, the destructive spirit better known in Middle Persian as Angra Mainyu's counterpart, and as a figure connected with the origin of menstruation.
The mythology appears most fully in later Zoroastrian religious literature, including the Bundahishn. In one account, Ahriman awakens from impotence after Jahi's incitement and defiles her with a kiss; the episode is often interpreted as a euphemistic description of sexual union. Jahi is then appointed to defile women, while menstruation itself is treated as part of the destructive creation associated with Ahriman.
Jahi should not be confused with Nasu, the female demon linked with the pollution of corpses. Az is another demonic figure associated with greed or insatiability, while Druj represents falsehood and deceit. Jahi is therefore the canonical answer for this question.