This question has two answers based on the marital status of the woman.
1- Assuming that the woman is married.
Marriage is a contract between two people on sharing the responsibilities of a mutual life. If the absence of one party means a default on that party’s share of responsibility, it requires the other party’s consent. If the other party, which in this case the husband gives consent, then she can go. The woman cannot do this without her husband’s consent. Men’s situation is not the same for various reasons, but it is not the subject of this fatwa.
2- Assuming that the woman is single and adult.
The only responsibility of the woman is to inform her Wali and show an effort to get his consent. Wali should be one from these respectively: father, brother, uncle, or someone close and is able protect her rights when needed. This is for the safety of her. She is not bound to anybody’s approval.
For travelling alone of women, please see the link below: