All perfect praise be to Allaah, the Lord of the worlds. I testify that there is none worthy of worship except Allaah and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
It is permissible to wear such a black headband, even if it is worn as an adornment. It is part of the external adornment that a woman is permitted to expose, as long as it does not involve imitation of men. Allaah Almighty says (what means): {And not expose their adornment except that which [necessarily] appears thereof.} [Quran 24: 31]
Commenting on the verse, Haafith Ibn Katheer said:
It means that they should not show any part of their adornment to non-Mahram (permanently unmarriageable) men except for whatever cannot be hidden thereof. Ibn Mas‘ood said, 'such as clothes and outer garments,' meaning such as what Arab women used to wear of the cloak that covered their clothes. Whatever showed from underneath the outer garment, however, there is no blame on her for this, because this is something that she cannot conceal.
However, a Muslim woman has to be cautious of impermissible exposure of adornment as well as everything that is likely to cause temptation. She should not go out of her home unless for a necessary need. When going out, she is required to wear the legitimate Hijab.
Thus, wearing this headband is permissible, as long as there is no imitation of men involved.
Allaah Knows best.