I believe that it is not permissible to wear it out in the public but it is permissible to wear it in front of other women.
Here is the fatwa of Sheikh Al Munajjid:
What is the ruling on women wearing high heels? Praise be to Allaah. Wearing high heels is not permissible because it exposes women to the risk of falling, and we are commanded in sharee’ah to avoid danger in a general sense, as Allaah says (interpretation of the meaning): “And do not kill yourselves” [al-Nisa’ 4:29] “and do not throw yourselves into destruction” [al-Baqarah 2:195] It also makes women look taller than they really are and makes their posteriors appear more prominent, and this is a kind of deception and showing the adornments which the believing woman is forbidden to show, as Allaah says (interpretation of the meaning): “and not to show off their adornment except only that which is apparent (like both eyes for necessity to see the way, or outer palms of hands or one eye or dress like veil, gloves, headcover, apron), and to draw their veils all over Juyoobihinna (i.e. their bodies, faces, necks and bosoms) and not to reveal their adornment except to their husbands, or their fathers, or their husband’s fathers, or their sons, or their husband’s sons, or their brothers or their brother’s sons, or their sister’s sons, or their (Muslim) women (i.e. their sisters in Islam)” [al-Noor 24:31] 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.
