Praise be to Allah.
It is permissible for her to wear perfume if she is going out to a women’s gathering and she will not pass by any men en route. But going out wearing perfume to market-places where there are men is not permitted, because the Prophet (peace and blessings of Allaah be upon him) said: “Any woman who has applied bukhoor (incense) should not attend ‘Ishaa’ (prayers) with us.” And there are other ahaadeeth concerning this matter. That is because if she goes out wearing perfume to places where men walk or places where men gather such as the mosques, this causes temptation to them. She must also cover herself and avoid wanton display (tabarruj), because Allaah says (interpretation of the meaning):
“And stay in your houses, and do not display yourselves like that of the times of ignorance”
Tabarruj includes showing the sites of temptation and beauty such as the face, head, etc.