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 is His slave and Messenger.
This operation is not included in what is called cosmetic surgery; rather, it is a kind of treatment, and seeking treatment is permissible. The Prophet said: “Each sickness has a remedy. So, when the appropriate remedy is given to the illness it gets cured by the Will of Allah, the Almighty.” [Muslim]
Therefore, it is permissible to carry out this operation if it does not cause any harm.
Allaah Knows best.