[The Ruling on a Person Selling His Kidney to a Patient]

The answer—and by Allah’s enabling: Transferring blood and organs from one person to another are newly arising matters for which the Lawgiver has not set down rulings specific to them. However, in our upright religion there are universal principles under which these newly arising issues may be subsumed and from which their rulings may be derived—such as Allah’s saying, after mentioning some prohibitions: “…excepting that to which you are compelled.” [Al-Anʿām:119], and His saying: “And do not kill yourselves.” [An-Nisā’:29], and the hadith: “No harm and no reciprocating harm,” along with what is known of the sanctity and great dignity of the Muslim, living and dead. On that basis we may say:
It is established that a Muslim may remove surplus blood from his body by cupping (h ija mah), and it is well known about the Prophet—May Allah bless him and his family and grant them peace—that he used to undergo cupping; there is no disagreement about its permissibility.
Accordingly, it is permissible for a Muslim to remove surplus blood; and, in cases of necessity, it is permissible to benefit from that blood, and for the one compelled to it to purchase it and benefit from it in his body. As for the one who provides the blood, it is not proper for him to take a price for what he has given of blood; however, there is no harm in compensating him for that—not as a sale price, but as an act of kindness.
— It is permissible for a Muslim to donate one of his kidneys to a patient in need of a kidney, on condition that a qualified specialist determines that removing his kidney entails no danger to his health, either presently or in the future.
— A Muslim may receive compensation in return for his donation of a kidney; it is not proper that he take a sale price for it on the basis of buying and selling.
— If taking an organ from a deceased person would save the life of a Muslim, it is permissible with the permission of the heirs—for example, to take the deceased’s heart and give it to the sick Muslim.
Source: Min Thimār al-ʿIlm wa al-Ḥikmah vol.2