Question

Were women cursed with menstruation?

Answer

Were women cursed by any sage or god with menstruation? What is the story of women being cursed with menstruation?

I think that is not a curse given to women by any sage or god, but women themselves accepted the menstruation cycle to make Indra free of his sin along with Prithivi, Jal, and Vruksha (earth, water and trees).

There is a story described in Shreemad Bhagvat Purana of Indra killing Vishwroopa and to get rid of the sin, he distributed his sin of killing a brahmana (Brahma-Hatya) in four parts to women, water, trees and earth. Shreemad Bhagvat Book 1, skandha 6, chapter 9:

ब्रह्महत्यामज्त्रलिना जग्राह यदपीश्वर |
संवत्सरान्ते तदघं भूतानां स विशुद्धते |
भूम्यम्बुद्रुमयोषिद्भ्यच्श्रतुर्धा वयभजद्भरि: ||६||

brahma-hatyām añjalinā jagrāha yad apīśvaraḥ
saṁvatsarānte tad aghaṁ bhūtānāṁ sa viśuddhaye
bhūmy-ambu-druma-yoṣidbhyaś caturdhā vyabhajad dhariḥ

Although Indra was so powerful that he could neutralize the sinful reactions for killing a brāhmaṇa, he repentantly accepted the burden of these reactions with folded hands. He suffered for one year, and then to purify himself he distributed the reactions for this sinful killing among the earth, water, trees and women. SB 6.9.6

This is further confirmed in another chapter, Skandha 6 chapter 13 shloka 5:

Indra said

स्त्रीभूजलद्रुमैरेनो विश्वरुपधोद्भ्वम् |
विभक्तमनुह्णद्भिर्व्रुत्रहत्यां क्व माज्म्यर्यहं ||५||

strī-bhū-druma-jalair eno viśvarūpa-vadhodbhavam
vibhaktam anugṛhṇadbhir vṛtra-hatyāṁ kva mārjmy aham

King Indra replied: When I killed Viśvarūpa, I received extensive sinful reactions, but I was favored by the women, land, trees and water, and therefore I was able to divide the sin among them. But now if I kill Vṛtrāsura, another brāhmaṇa, how shall I free myself from the sinful reactions? SB 6.13.5

And here is your answer:

शश्र्वत्कांमवरेणामहस्तुरियं जगृहु: स्त्रिय:|
रजोरुपेण तास्वमहो मासि मासि प्रदृश्यते ||९||

śaśvat-kāma-vareṇāṁhas turīyaṁ jagṛhuḥ striyaḥ 
rajo-rūpeṇa tāsv aṁho māsi māsi pradṛśyate 

In return for Lord Indra’s benediction that they would be able to enjoy lusty desires continuously, even during pregnancy for as long as sex is not injurious to the embryo, women accepted one fourth of the sinful reactions. As a result of those reactions, women manifest the signs of menstruation every month. SB 6.9.9

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