Hair transplant refers to moving the hair follicles from one area of a person’s head to another. The ruling on that is that it is permissible, because it is aimed at correcting a fault, not at changing the creation of Allaah.
Shaykh Muhammad ibn ‘Uthaymeen (may Allaah have mercy on him) was asked:
Hair transplants are done for one who has become bald by taking hair from the back of the head and transplanting it in the bald spot. Is that permissible?
Yes, that is permissible, because this comes under the heading of restoring that which Allaah has created, or correcting a fault; it does not come under the heading of cosmetic procedures or adding to what Allaah has created, so it is not regarded as changing the creation of Allaah. Rather it is restoring something that is lacking or removing a fault. There is the well-known story of the three people, one of whom was bald and said that he wished that Allaah would restore his hair, so the angel touched him and Allaah restored his hair and gave him beautiful hair.
Fatawa ‘Ulama’ al-Balad al-Haraam, p. 1185.
The hadeeth referred to by the Shaykh (may Allaah have mercy on him) was narrated by al-Bukhaari, 3277, and Muslim, 2964.
And Allaah knows best.