This is one of the most important and commonly asked questions for women performing Hajj. When Aisha (may Allah be pleased with her) began menstruating during her Umrah journey, the Prophet (peace be upon him) told her: 'Do everything that the pilgrim does, except do not perform Tawaf around the House until you are pure.' Based on this, the majority of scholars hold that Tawaf requires ritual purity and a menstruating woman must wait until her period ends to perform Tawaf.
The Hanafi school provides an exception for the obligatory Tawaf al-Ifadah: if a woman's travel group is departing and she cannot delay, she may perform Tawaf al-Ifadah while menstruating, but must sacrifice a camel (badanah) as a penalty. Some contemporary scholars, including Shaykh Ibn Taymiyyah, held that if a woman has no choice (her group is leaving, she cannot stay), she may perform Tawaf after securing protection against discharge and her Tawaf is valid without penalty — though this is a minority opinion.
Importantly, a menstruating woman remains in Ihram and can perform all other Hajj rituals normally: standing at Arafat, staying at Muzdalifah, stoning at Jamarat, Sa'i (according to some scholars), and making dua everywhere. She is exempted from the farewell Tawaf (Tawaf al-Wada) entirely — this is agreed upon by all scholars. Modern medical options such as medication to delay menstruation should be discussed with a doctor well before the trip.