In the Name of Allah, the All-Merciful, the Mercy-Giving
All praise is due to Allah. Peace and blessings be upon His Messenger Muhammad.
A menstruating woman can do hajj normally by doing all rituals with the exception of making tawāf. She can commence on the state of ihram, stand in Arafah, spend a part of the night in Muzdalifah and throw the jamarat in addition to going in between Ṣafa and Marwa.
She is prohibited to make tawaf during her menstruation. This is based on the report of Al-Bukhari and Muslim on the authority of ‘A’ishah that Safiyyah bint Huyayy, the wife of the Prophet (peace be upon him) got her menses during the Farewell Pilgrimage, and the Prophet (peace be upon him) said: “Is she detaining us?” Aishah said, “She has already done tawaf al-ifadah, O Messenger of Allah, and has circumambulated the Kabah.” So the Prophet (peace be upon him) said: “Then let her depart.”
This indicates that the menstruating woman is not allowed to do tawaf and that she should remain [in Makkah] until she becomes pure; if she leaves, then she must come back and do tawaf. This is the view of the majority of scholars.
In the case of a menstruating woman offering hajj, she can take medicine to delay her menstruation if it does not have any harm. This is reported from some female companions of the Prophet whose practice was approved by the Prophet.
In case she is menstruating during the time of obligatory tawaf, which is offered after standing in Arafa, she can delay it to make it at the end of her trip.
In this case, she can intend both the obligatory and farewell tawaf together. In case she will ultimately miss her flight, she can follow the fatwa of Imam ibn Taymiyyah. He was of the view that if she cannot stay in Makkah because she is part of a group that will leave soon, and she cannot come back in order to do tawaf, then in that case she has no choice, so she should take measures to prevent the blood from falling onto the ground, and do tawaf. Some of the scholars have issued fatwas to this effect. Allah, may He be exalted, says: “Allah intends for you ease and does not intend for you hardship” (Al-Baqarah 2:185)
Almighty Allah knows best.