This is one of the most important topics for women الحجاج. First, the reassuring news: menstruation does NOT invalidate your الحج or prevent you from completing it. النبي (صلى الله عليه وسلم) explicitly told Aisha when she began menstruating during her الحج: 'Do everything that the الحاج does, except do not perform الطواف around the House until you are pure.'
What you CAN do while menstruating: stand at عرفة (the most essential pillar of الحج), stay at مزدلفة, stone at الجمرات, make the animal sacrifice, remain in the state of الإحرام, make unlimited دعاء and dhikr, attend the عرفة sermon, and collect pebbles. Regarding السعي, some scholars (including the Hanbali school) permit السعي during menstruation since it does not take place inside the مسجد proper. The farewell الطواف (الطواف al-Wada) is completely waived for menstruating women — this is unanimous among all scholars.
The only challenge is الطواف al-Ifadah, which is a pillar of الحج and requires ritual purity عند the majority. Options include: (1) Wait until your period ends, purify, and perform الطواف — this is the safest approach if your schedule allows. (2) The Hanafi school permits performing الطواف al-Ifadah during menstruation with protection if departure cannot be delayed, but requires a camel sacrifice as penalty. (3) Consult a scholar about your specific situation.
Prevention strategy: many Muslim women use hormonal الأدوية to delay their period during the الحج days. Consult your doctor 2-3 months before departure to find a suitable option and trial it beforehand. This is جائز in Islamic law when done for a valid purpose like facilitating worship.