All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
If the nose is big within what is normally accepted and does not reach the extent of deformity, and its size only makes the person less beautiful, then it is not permissible to undergo a cosmetic plastic surgery to make it smaller. However, if the nose is too big to the extent that makes it deformed, then there is nothing wrong in performing this surgery to make it smaller, because this is considered as treatment and not an enhancement of one's beauty. The Islamic Fiqh Academy mentioned in a statement when it would be permissible to undergo cosmetic plastic surgeries and what it would not be, saying:
1) It is permissible to undergo a cosmetic plastic surgery when it is necessary and needed, and which is intended to:
a) Restore the shape of the body's organs to the normal state in which man was created, for Allah Almighty Says (what means): {We have certainly created man in the best of stature.} [Quran 95:4]
b) Restore the normal function to the body organs.
c) Repair physical defects, if it causes effective physical or psychological harm, such as: cleft lip, severe bending of a nose, birthmarks, excess fingers, excess teeth, and syndactyly.
d) Repair of circumstantial defects (did not exist at birth) such as ones resulting from burns, accidents, diseases and the like, such as:
* Skin transplantation and grafting,
* Completely reshaping of the breast after its removal, or partly reshaping it (breast) because it is too large or too small and can lead to a condition of illness,
* Hair transplantation in case of hair loss, especially in women.
* Removal of an ugly spot which causes physical or psychological harm.
2) It is not permissible to undergo cosmetic plastic surgery which is not done for treatment, and which is intended to change the shape of the normal person merely to fulfill one's desires or imitate others, such as changing the face shape to appear with a certain appearance or to deceive the justice system, changing the shape of the nose, enlarging or reducing the lips, changing the shape of the eyes, enlarging the cheeks, etc. [End of quote]
Allah Knows best.