And selling perfumes and bakhoor (incense) to men and women, and burning bakhoor in the store constantly so as to attract customers, when it is possible that some of the fragrance may get onto her, such as the bakhoor and perfumes that she is offering for sale?.
There is nothing wrong with a woman working in buying and selling, so long as she adheres to proper Islamic etiquette in her dress, speech and dealings.
In the early days of Islam, women used to buy and sell in a modest and reserved manner, and none of the scholars objected to that.
In Fataawa al-Lajnah al-Daa’imah (17/13), it says:
It is permissible for her (a woman) to go to the marketplace to buy and sell, if she needs to do so, and if she covers her entire body in clothes that do not show her shape, and she does not mix freely with men. But if she does not need to engage in that buying and selling, then it is better for her not to do that. End quote.
But if a woman’s engaging in trade will lead to her uncovering that which Allah has forbidden her to uncover, such as her face, or to her travelling without a mahram, or to her mixing with non-mahram men in a manner that it is feared will lead to fitnah, then it is not permissible for her to do that; rather she should not do it. End quote.
Fataawa al-Lajnah al-Daa’imah, 13/16
For a woman to work in a perfume shop, selling to men, exposes her to fitnah and may encourage foolish men to approach her.
There is nothing wrong with a woman selling perfume and bakhoor so long as she is careful not to let any of the fragrance get onto her, because of the warning against women wearing perfume in front of non-mahram men. See the answer to question no. 102329.
And it is not permissible for her to burn bakhoor in her shop to attract customers, because the fragrance of the bakhoor will undoubtedly get onto her, and the Prophet (blessings and peace of Allah be upon him) said: “Any woman who has got the fragrance of bakhoor on her should not attend ‘Isha’ prayer with us.”
Narrated by Muslim, 444.
If the woman who is going to the mosque is forbidden to use perfume and bakhoor, then how about the one who is sitting in the marketplace to buy and sell, where men will inevitably smell the fragrance of bakhoor from her?
So it is better for that woman, if she needs to work, to limit it to selling to women only, so that she will not mix with men.
And Allah knows best.