Praise be to Allaah.
Shaykh Ibn Baaz (may Allaah have mercy on him) was asked about that and he said:
“I do not know of any reason not to do that, because Allaah says in His Book (interpretation of the meaning):
“Allaah does not forbid you to deal justly and kindly with those who fought not against you on account of religion nor drove you out of your homes”
So Allaah tells us that He does not forbid us to deal justly and kindly with those kaafirs who are not fighting us and who have not driven us out of our homes, or with those who are in urgent need of help. The mother of Asmaa’ bint Abi Bakr al-Siddeeq (may Allaah be pleased with her) came to her daughter in Madeenah, at the time of the peace treaty between the Prophet (peace and blessings of Allaah be upon him) and the people of Makkah, and she was still a kaafir, to ask her to uphold the ties of kinship. Asmaa’ consulted the Prophet (peace and blessings of Allaah be upon him) and he told her to uphold the ties of kinship, saying, “Uphold the ties of kinship with your mother even though she is a kaafir.”
If a kaafir who has a peace treaty with the Muslims or is under the protection of the Muslims, and is not hostile towards Islam and is not in a state of war with us is in urgent need, then there is nothing wrong with giving blood to him. You will be rewarded for that, because there is nothing wrong with you helping one who is in urgent need of charity or help.
From Kitaab Fataawa Noor ‘ala al-Darb, vol. 1, p. 376
Based on the above, if the kaafir is hostile or in a state of war with the Muslims, then it is not permissible to give him blood, because by doing so you are helping him in his aggression against the Muslims. This is a very serious matter. We ask Allaah to keep us safe and sound.