Menstruation is a monthly discharge that every woman experiences during her lifetime when she is actively reproducing. It is one of the orders by Allah given to women, and when it comes, they are restricted from performing some obligatory religious duties, e.g., observing Solat and fasting in the month of Ramadan, among others. Now, the question is, can a woman in her monthly discharge perform hajj? The answer is yes, except that such a woman in that condition will not circumambulate the Ka’ba.
We get to know this by the hadith collected by Bukhari as narrated by Al-Qasim: `Aisha said, “We set out with the sole intention of performing Hajj and when we reached Sarif, (a place six miles from Mecca) I got my menses. Allah’s Messenger (SAW) came to me while I was weeping. He said ‘What is the matter with you? Have you got your menses?’ I replied, ‘Yes.’ He said, ‘This is a thing which Allah has ordained for the daughters of Adam. So do what all the pilgrims do with the exception of the Tawaf (Circumambulation) round the Ka`ba.” `Aisha added, “Allah’s Messenger (SAW) sacrificed cows on behalf of his wives.”
Sahih al-Bukhari, 294
Therefore, this is evident enough for menstrual women to perform hajj, but with the exception stated in the hadith above.