This is one of the most important and commonly asked questions for women performing Hac. When Aisha (may Allah be pleased with her) began menstruating during her Umre journey, Hz. Peygamber (sallallahu aleyhi ve sellem) told her: 'Do everything that the haci does, except do not perform Tavaf around the House until you are pure.' Based on this, the majority of scholars hold that Tavaf requires ritual purity and a menstruating woman must wait until her period ends to perform Tavaf.
The Hanafi school provides an exception for the farz Tavaf al-Ifadah: if a woman's travel group is departing and she cannot delay, she may perform Tavaf 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 Tavaf after securing protection against discharge and her Tavaf is valid without penalty — though this is a minority opinion.
Importantly, a menstruating woman remains in Ihram and can perform all other Hac rituals normally: standing at Arafat, staying at Muzdelife, stoning at Cemerat, Say (according to some scholars), and making dua everywhere. She is exempted from the farewell Tavaf (Tavaf 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.