According to Shaikh ibn Uthaimim, they are not allowed since they are besides the norm and they lead the woman to expose her beauty and make people look at her. Allah (SWT) has said:
Do not display yourselves like that of the times of ignorance. (al-Ahzab 33)
Everything that leads the woman to displaying herself and showing her beauty and in such a beauteous way distinguishing herself from the other women is forbidden and not allowed.
And according to another scholar, Sheikh Ibn Baz:
“The least that can be said is that it is disliked.
• First, it is a kind of deception because it makes the woman look taller than she is.
• Second, it is dangerous for the woman because it is easy to fall in them.
• Third, it has negative health consequences as the doctors have concluded.”
It has also been proven that the woman’s hips actually swing more with high heels as well thus contributing to the act of Tabarruj (displaying beauty and ornaments to strangers.
From Fataawa al-Lajnah al-Daa’imah, Majallat al-Buhooth, 9/46.
Moreover, it also makes a woman lean forward (maa’ilah ila al-amaam), so there is the fear that the warning issued to those women who walk with an enticing gait (al-maa’ilaat al-mumilaat) may apply to her too [in the hadeeth which says that such women will never even smell the fragrance of Paradise from afar]. It also harms the back, as has been proven medically. The heels also make a sound which attracts the attention of men and is a temptation to them. We ask Allaah to keep us all safe and sound.
Sheikh Muhammed Salih Al-Munajjid