Praise be to Allah.
Wearing high heels is not permissible because it exposes women to the risk of falling, and we are commanded in the Shari`ah to avoid danger in a general sense, as Allah 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]
Wearing high heels 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 Allah 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 Juyubihinna (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-Nur 24:31] (Fatawa al-Lajnah al-Daimah, Majallat al-Buhuth, 9/46)
Moreover, wearing high heels also makes a woman lean forward, so there is the fear that the warning issued to those women who walk with an enticing gait (al-mailat al-mumilat ) may apply to her too [in the hadith which says that such women will never even smell the fragrance of Paradise from afar].
It has been proven medically that wearing high heels harms the back. The heels also make a sound which attracts the attention of men and is a temptation to them. We ask Allah to keep us all safe and sound.
And Allah knows best.