It is permissible for women to wear bras so long as they are not tight or thin and show the size of the breasts, unless that is in front of her husband or she wears over it a loose, wide garment that covers it.
That is because women are enjoined to cover their ‘awrah with something that cannot be seen through and that does not show the shape.
Ahmad (21834) narrated that Usaamah ibn Zayd (may Allah be pleased with him) said: The Messenger of Allaah (peace and blessings of Allaah be upon him) gave me a thick Egyptian garment that was one of the gifts given to him by Dihyah al-Kalbi, and I gave it to my wife to wear. He said, “Why do I not see you wearing that Egyptian garment?” I said, I gave it to my wife to wear. He said, “Tell her to wear a gown underneath it, for I am afraid that it may describe the size of her bones.” Narrated by al-Bayhaqi in al-Sunan al-Kubra (2/234); classed as hasan by al-Albaani in Jilbaab al-Mar’ah al-Muslimah, p. 131.
The scholars of the Standing Committee for Issuing Fatwas were asked: What is the ruling on women wearing bras?
Wearing bras that define the breasts and give them a shape and make women look young provokes a lot of fitnah; it is not permissible for a woman to appeal wearing it in front of men who are strangers (non-mahrams) to her. End quote.
Fataawa al-Lajnah al-Daa’imah, 17/107
Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) said: With regard to bras, there is nothing wrong with a woman wearing something to beautify her breasts. There is nothing wrong with that but I think that a young woman who is not married should not wear it because in that case it will develop in her a love of showing off, which may lead to temptation and she should not do that. But if a married woman does that for her husband, there is nothing wrong with that and it is regarded as coming under the heading of beautification. End quote from Fataawa Noor ‘ala al-Darb.
And Allah knows best.