The scholars of the Standing Committee said:
A woman who does not have a mahram does not have to do Hajj, because in her case a mahram is part of being able to do Hajj, and being able to do it is one of the conditions of Hajj being obligatory.
Allaah says (interpretation of the meaning): “And Hajj (pilgrimage to Makkah) to the House (Ka‘bah) is a duty that mankind owes to Allaah, those who can afford the expenses (for one’s conveyance, provision and residence)” [Aal ‘Imraan 3:97] It is not permissible for her to travel for Hajj or for any other purpose unless she is accompanied by her husband or a mahram, because of the report narrated by al-Bukhaari and Muslim from Ibn ‘Abbaas (may Allaah be pleased with him), that he heard the Prophet (Sallallahu alaihi wa sallam) say:
“No man should be alone with a woman unless her mahram is present, and no woman should travel unless she has a mahram with her.”
A man stood up and said: “O Messenger of Allaah, my wife has gone out for Hajj, and I have enlisted for such and such a campaign.” He said: “Go and do Hajj with your wife.”
This was also the view of al-Hasan, al-Nakha’i, Ahmad, Ishaaq, Ibn al-Mundhir and ashaab al-ra’i, and it is the correct view, because of the verse quoted, as well as the general meaning of the ahaadeeth which forbid a woman to travel without her husband or a mahram.
Maalik, al-Shaafa’i and al-Awzaa’i held a different opinion and each of them stipulated a condition (allowing her to do that), but with no evidence. Ibn al-Mundhir said: they did not follow the apparent meaning of the hadeeth, and each of them stipulated a condition (allowing her to do that), but with no evidence. Fataawa al-Lajnah al-Daa’imah li’l-Buhooth al-‘Ilmiyyah wa’l-Ifta’, 11/90, 91