As far as Islamic Sharia is concerned, a Muslim woman is not allowed to wear perfume in public with the intention of attracting others. The Prophet (peace and blessings be upon him) is reported to have said, “If a woman wears perfume and then passes by people who smelled her perfume, she is then considered an adulteress. And every eye is liable to commit adultery.” (al-Sunan al-Kubrah). This hadith does not mean that a woman who does that will be considered as having fornicated or committed adultery; rather, it is a forewarning for women not to wear perfume in public.
Responding to this issue, Zeinab Al-`Alawani, an Instructor of Fiqh and Islamic Studies, states:
The hadith contains a warning and a strong-toned statement for any attempt to cause moral corruption in the Islamic society.
In Surat An-Nur, the Qur’an laid down many protective measures to safeguard morals and prevent adultery and fornication in society. These measures have been implemented and translated into practice by the Prophet (peace and blessings be upon him).
With regard to perfume, make-up, and so on, they are sources of temptation that can open the gate to illicit behavior and relationships outside the framework of marriage, thereby spreading illegal sexual intercourse in society. Therefore, the hadith does not speak about the woman as having committed illegal sexual intercourse, but doing something that might lead to it, namely temptation.