Is Uterus Transplant Allowed in Islam?
Question

What is the ruling on transplantation of the uterus and ovaries?
Praise be to Allah.Ruling on Uterus Transplantation
There is nothing wrong with uterus transplantation for a woman who has lost her uterus or is not able to bear children.
A statement to that effect was issued by the Islamic Fiqh Council, in which it says:
Transplantation of some reproductive organs that do not transmit hereditary characteristics, with the exception of the most private parts, is permissible on the basis of necessity according to Islamic teachings, and in accordance with the guidelines and standards prescribed in Islamic teachings.” (End quote from Qararat wa Tawsiyaat Majma` Al-Fiqh Al-Islami, p. 121)
The uterus does not carry any hereditary characteristics concerning which there is the fear that they may be transmitted to the recipient of the transplant; rather it is more akin to a vessel in which the foetus grows.
The Role of the Ovary in Reproduction and Heredity
The ovary is the female reproductive organ, and is the counterpart of the testicle in men. The ovary performs two functions:

It is a gland which secretes female hormones which are essential to a woman’s femininity.
From the time the woman reaches puberty until menopause, the ovary produces the eggs which are essential for pregnancy to occur in the presence of sperm from the male.

Why Ovary Transplantation is Prohibited in Islam
These eggs carry hereditary traits, which differ from one woman to another. If we assume that this operation is successful and the ovary of one woman is transplanted in another, then it will be carrying hereditary traits from one woman to another woman who is a complete stranger to her, and thus this is regarded as mixing lineages.” (End quote from Majallat Majma` Al-Fiqh Al-Islami, 6/3/1980)
The ovary is the organ that is responsible for producing eggs, and it is like the seed of a woman from which her traits and the traits of her forebears are transmitted to her offspring.
Hence the Islamic Fiqh Council issued a statement that it is prohibited to transplant ovaries, in which it says:
As the testicles and ovaries continue to carry and secrete the hereditary traits (the genetic code) of the one from which they are taken, even after they are transplanted into a new recipient, transplantation of both is prohibited according to Islamic teachings.” (End quote from Qararat wa Tawsiyat Majma` Al-Fiqh Al-Islami, p. 121)
For more details, please see the following answers: 2117, 107690, 47664, 481783, 2160.
And Allah knows best.