It was narrated by Imam Ahmad (40/229), and by al-Tirmidhi (2786) who classed it as saheeh, that Abu Moosa al-Ash’ari (may Allah be pleased with him) said: The Messenger of Allah (blessings and peace of Allah be upon him) said: “Any woman who puts on perfume then passes by the people so that they can smell its fragrance is a zaaniyah.” Classed as hasan by al-Albaani.
Al-Haafiz Ibn Hajar (may Allah have mercy on him) said:
Women are enjoined to cover themselves when they go out of their houses, and the perfume which has a fragrance is not allowed because it increases the fitnah. End quote.
It was narrated by Abu Dawood (2174), and by al-Tirmidhi (2787) who classed it as hasan, that Abu Hurayrah (may Allah be pleased with him) said: The Messenger of Allah (blessings and peace of Allah be upon him) said: “Perfume for men is that which has a strong fragrance and scant colour, and perfume for women is that which has a strong colour and scant fragrance.” Classed as saheeh by al-Albaani in Saheeh al-Tirmidhi.
Sa’eed ibn Abi ‘Uroobah, the narrator of the hadeeth, said: I think that with regard to the words “perfume for women” this refers to when she wants to go out, but if she is with her husband, she may apply whatever perfume she wants. End quote.
Sunan Abi Dawood (4/84); Sharh al-Sunnah by al-Baghawi, 12/81. See: al-Mawsoo’ah al-Fiqhiyyah, 12/174
To sum up: if a woman wants to go out of her house, she must avoid wearing perfume that has a strong fragrance, if she is going to pass by groups of men or is in a place where she will mix with them. This ruling does not apply only to one kind of perfume and not another; rather what counts here is whether the fragrance can be smelt by any man.
Whatever comes under the same heading as using fragrance, such as using soap or shampoo that has a strong and lasting smell that remains after using it, comes under the same ruling. It is not permissible for her to use any of those things if she is going out of her house or mixing with men.
Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) said:
There are things that are perfumed which in and of themselves are not perfume, but they are perfumed, so they come under the same ruling as that which is perfume in and of itself, such as some soaps that have a clear fragrance and not just a scent; rather it is perfume, such that if a person were to wash with it, its fragrance would be clear on his hand. This comes under the same ruling as perfume. As for a mere scent which if a person washes with it, it does not leave a smell, there is nothing wrong with this -- meaning for the muhrim (pilgrim in ihram). End quote.
Sharh al-Kaafi, 1/112
And Allah knows best.
For more information please see the answer to question number 102329.