If there is severe overcrowding in which there is fear for women, it is not permissible for a woman to join that crowd, because that is exhausting for her and because she is going to stone the Jamrah without being able to focus on the action because of the severity of the crowding. For example, if the people want to hasten on and depart after two days, and they have to stone the Jamaraat when the sun reaches its zenith and then depart, in this case it is not possible for the woman to stone the Jamaraat all, because it is dangerous for her. So in this case we say: Delegate someone (to stone the Jamaraat on your behalf), and there is nothing wrong with that. But in other cases, such as on the eleventh day (of Dhu’l-Hijaah), it is possible to delay the stoning from the meridian until the time of ‘Asr or until the night, and even until dawn. So the matter is broad in scope, praise be to Allah.
Majmoo‘ Fataawa Ibn ‘Uthaymeen (23/122).
The scholars of the Standing Committee for Issuing Fatwas were asked: Is it permissible to stone the Jamaraat during the day of Hajj nowadays on behalf of women, because of the severe overcrowding?
Allah, may He be exalted, say (interpretation of the meaning):
“Allaah intends for you ease, and He does not want to make things difficult for you”
“Allah does not want to place you in difficulty”
Hardship and difficulty are not the nature of this religion by virtue of these two verses and similar texts. And women’s situations vary: some may be pregnant and physically very large, or they may be emaciated, or sick, or elderly, and some may be strong. In the case of a woman who has one of the excuses referred to or something similar to that, it is permissible to appoint someone (to stone the Jamaraat) on her behalf, and there is no problem with that. The one who does the stoning on her behalf should not do that until after getting her permission before he (stones the Jamaraat) on her behalf. So he should throw stones on his own behalf first, then on her behalf. As for the one who is strong, if the hardship involved is extraordinary, it is permissible to appoint someone to do the stoning on her behalf in the same manner as described above; he should throw stones on her behalf after doing so on his own behalf. The person who does the stoning on another person’s behalf should be a fellow pilgrim.
And Allah is the source of strength. May Allah sent blessings and peace upon our Prophet Muhammad and his family and companions. End quote.
Fataawa al-Lajnah al-Daa’imah, 11/283
It also says (11/284):
When it is very crowded, it is permissible for a woman to appoint someone to stone the Jamaraat on her behalf, even if her Hajj is the obligatory Hajj. That may be done if she is sick or weak, or so as to protect her pregnancy if she is pregnant, and to protect her honour and dignity, so that it will not be transgressed because of the severe crowding.
Standing Committee for Academic Research and Issuing Fatwas.