Reference: Fataawa al-Lajnah ad-Daa.imah lil-Buhooth al-‘Ilmiyyah wal-Iftaa., – Volume 5, Page 182, Question 1 of Fatwa No.6259
Fataawa wa Ahkaam fee Sha’r an-Nisaa – Question 28, Page 33
Question: My wife complains of her hair falling out a lot and it was said to her to cut it short as this will reduce the falling out [of the hair]. Is this permissible?
Response: If the situation is as mentioned, then it is permissible [to cut the hair short] since this will prevent further harm.
And with Allaah lies all success and may Allaah send prayers and salutations upon our Prophet Muhammad ﷺ and his family and his companions.