Praise be to Allah.
Shaykh Muhammad ibn Ibraaheem Aal al-Shaykh (may Allaah have mercy on him) answered this particular question as follows:
In order to answer this question, we need to discuss three matters:
1.Who is the person who is to receive the blood transfusion?
2.Who is the person from whom the blood is to be taken?
3.Who is the person whom we can trust to decide whether a blood transfusion is needed?
With regard to the first question, the person who is to receive the blood transfusion is a person whose life is in danger due to sickness or injury, and whose life depends on his receiving a blood transfusion.
The principle in this matter is based on the following aayaat of the Qur’aan (interpretation of the meanings):
“He has forbidden you only the maytatah (dead animals), and blood, and the flesh of swine, and that which is slaughtered as a sacrifice for others than Allaah. But if one is forced by necessity without willful disobedience nor transgressing the limits, then there is no sin on him…” [al-Baqarah 2:173]
“… But as for him who is forced by severe hunger, with no inclination to sin (such can eat these above-mentioned meats), then surely, Allaah is Oft-Forgiving, Most Merciful.” [al-Maa’idah 5:3]
“… He has explained to you in detail what is forbidden to you, except under compulsion of necessity…” [al-An’aam 6:119]
The evidence derived from these aayaat tells us that if the recovery of the sick or injured person depends on a blood transfusion which he needs to save his life, and that there is no other medicine or food that can do the same thing, then it is permissible for him to receive a blood transfusion. In fact, this comes under the heading of nourishment, not medicine (using forbidden foodstuffs in cases of necessity is permissible, as in the case of a starving man eating dead meat).
With regard to the second point, the one from whom blood is taken, this should not result in any serious harm, because the Prophet (peace and blessings of Allaah be upon him) said: “There should be no causing harm or reciprocating harm.”
As regards the third point, which is the matter of whose opinion should be relied upon to decide whether a blood transfusion is needed, this should be a Muslim doctor. If that is not possible, we see nothing wrong with taking the word of a non-Muslim doctor, whether he is Jewish or Christian (or any other religion), so long as he is experienced in medicine and is trustworthy. The principle here is the saheeh hadeeth which describes how the Prophet (peace and blessings of Allaah be upon him) hired a man of Bani Deel as a skilled and experienced guide, although he was a follower of the pagan religion of Quraysh. (Reported by al-Bukhaari, 2104.) (Fataawa al-Shaykh Muhammad ibn Ibraaheem).
Concerning this matter, the Hay’at Kibaar al-‘Ulamaa’ (Council of Senior Scholars) stated the following:
1.It is permissible to donate blood, so long as this does not cause him any harm, when there is a need for it to help other Muslims.
2.It is permissible to establish Islamic blood banks to receive and store donated blood, to be kept for any Muslim who may be in need of it, so long as no money is charged to the sick person or the people in charge of his affairs in return for this service. A blood bank should not be set up as a commercial enterprise or a means of making money, because it is in the public interest of the Muslims.