All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.
There is no disagreement among the scholars concerning the permissibility of making Ruqyah (reading Qur'an and Prophetic supplications) to non-Muslims. The evidence for this is the narration of Abu Sa'eed Al-Khudri who said that they came during a journey to a tribe of Arabs, who refused to host them. But, the leader of the tribe was bitten by a snake; they (the tribesmen) came to the companions and asked them to do Ruqyah for him. The companions refused to do so unless they paid them a wage for it. They agreed to give them a flock of sheep. The companions then made the Ruqyah and the leader of that tribe was cured. When they came to the Prophet Sallallaahu Alayhi wa Sallam, he said: "What you did is correct and make one share for me too." [Muslim]
The narration proves that making Ruqyah for a non-Muslim is allowed. As for the verse (interpretation of the meaning): {And We send down from the Qur'aan that which is a healing and a mercy to those who believe (in Islaamic Monotheism and act on it), and it increases the polytheists (and wrong-doers) nothing but loss.}[17:82], it does not prevent making Ruqyah for non-Muslims. The meaning of this verse is as explained by Abu Qataadah, if a Muslim listens to the Qur'an, he benefits from it while a disbeliever does not benefit from that. A believer is cured from doubts, hypocrisy, and other spiritual diseases while a disbeliever does not get such a cure.
Allaah knows best.