In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
In this fatwa:
Answering your question, the Fatwa Center at Islam Q and A, states:
It is permissible for a woman to remove facial hair by laser, subject to certain conditions:
1- That this is done by a specialist female doctor. It is not permissible for it to be done by a male doctor except in the case of necessity.
2- That no harm results from using the laser, because of the general meaning of the words of the Prophet (peace be upon him), “There should be neither harming nor reciprocating harm.” (Ibn Maajah)
Concerning that, reference should be made to specialists. Ibn Muflih (may Allah have mercy on him) said in Al-Adaab ash-Shar`iyyah (3/97):
“It is haram to treat sickness or apply to the eyes anything that is impure, pure but haram, or harmful, and so on.”
3- That should not involve extravagant or wasteful spending; rather the hair should be removed by the normal means by which it is removed in such cases, with no need for spending large amounts of money, for something concerning which the most that can be said is that it is permissible or an adornment, whilst noting that some scholars differ as to whether it is even permissible in the first place.
Moreover, it makes no difference in the ruling whether that is done in Ramadan or otherwise; rather whatever is permissible at times other than Ramadan does not become prohibited by fasting.
Almighty Allah knows best.