As regards this question, Dr. Muzammil Siddiqi, former president of the Islamic Society of North America, states the following:
“This issue is very much debated by the jurists in past two decades. The Supreme Council of `Ulama in Riyadh (in their resolution no. 99 dated 6 Dhul Qi’dah 1402) has allowed both organ donation and organ transplantation in the case of necessity.
the organ can be taken from the body of a living person with his/her consent and approval and also from the body of a dead person. In the case of a living person, the jurists have stipulated that this donation should not deprive him/her of vital organs. It should also not cause risk to his/her normal life.
the Fiqh Academy of the Muslim World League, Makkah also allowed organ donation and transplantation in its 8th session held between 28 Rabi’ul Thani- 7 Jumadal Ula, 1405.
the Fiqh Academy of the Organization of the Islamic Conference in Jeddah, during the year 1408, and the Mufti of Egypt Dr. Sayyed At-Tantawi also allowed the use of the body organs of a person who has died in an accident, if the necessity requires the use of any organ to cure a patient, provided that a competent and trustworthy Muslim physician makes this decision.
It is important to note that most of the jurists have only allowed the donation of the organs. They do not allow the sale of human organs. Their position is that the sale of human organs violates the rules of the dignity and honor of the human being, and so it would be haram in that case.
Some jurists suggest that because people have become too materialistic and it may not be possible to find a free organ, under necessity one can purchase the organs, but a Muslim should never sell his/her organs.”
May Allah guide all of us to what pleases Him!