Assalaamu alaykum wa rahmatullaahi wa barakaatuhu, Shaykh. If a woman feels uncomfortable among men in a crowd (especially because I have seen bad things among a lot of people in this world), is it better for her to stay at a distance from the Ka‘bah, where the crowd is less, while doing Tawaaf (circumambulation)? May Allaah reward you, Shaykh.
All perfect praise be to Allah, The Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallahu ‘alayhi wa sallam, is His slave and Messenger.
There is no doubt that it is better for the woman to not crowd with men and keep away from them while doing Tawaaf; she may do Tawaaf beyond them, even if it is at a distance from the Ka‘bah. Umm Salamah, may Allah be pleased with her, said, "I complained to the Messenger of Allah, sallallahu ‘alayhi wa sallam, of my ailment, whereupon he said, 'Perform Tawaaf beyond the people while riding.' So I performed Tawaaf while the Messenger of Allah, sallallahu ‘alayhi wa sallam, was at that time praying towards the side of the House and reciting Soorah At-Toor (Chapter 52)." [Al-Bukhari and Muslim]
Ibn Hajar said, "He ordered her to perform Tawaaf beyond the people so that she would be more screened (from men) and so that she would not cut their lines."
Al-Baaji wrote in his commentary on Al-Muwatta', "It is an act of the Sunnah for the woman to perform Tawaaf beyond the men, because Tawaaf is an act of worship related to the Ka‘bah; so it is an act of the Sunnah for women to perform Tawaaf behind the men, just like they perform the prayer behind the rows of men."
It is narrated in Saheeh Al-Bukhari that Ibn Jurayj asked ‘Ataa', "How could they (women) mix with the men?" ‘Ataa' said, "They did not mix (with the men); ‘Aa'ishah, may Allah be pleased with her, used to perform Tawaaf at a good distance from the men and did not mix with them." [Saheeh Al-Bukhari]
Allah knows best.
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