When visiting a non-Muslim sick, a Muslim is permitted to make du`aa’ for him or her the same way he makes du`aa’ for a Muslim. Prophet Muhammad (peace and blessings be upon him), who was sent as a mercy for all humankind, gave us prime example in visiting the sick from among non-Muslims and setting an ideal example for them and helping them find the true path.
Sheikh Mohamed El-Moctar El-Shinqiti, director of the Islamic Center of South Plains, Lubbock, Texas, US, states, Imam Al-Bukhari reports that Prophet Muhammad (peace and blessings be upon him) used to say this du`aa’ (Arabic for: supplication) for people who are sick, whether he was visiting the sick person or the person was brought to him.
Adh-hibi al-ba’sa, Rabba an-nas, ishfi wa anta ash-shafi, la shifaa’ illa shifa’uka, shifa’an la yughadiru saqaman (Arabic for: Remove the affliction, O Lord of Humankind, and send down cure and healing, for no one can cure but You; so cure in such a way that no trace of illness is left).
The hadith does not distinguish between a Muslim and a non-Muslim. And since we know from other authentic hadiths that the Prophet (peace and blessings be upon him) visited some non-Muslims who were sick (including a Jewish boy, as Al-Bukhari himself reports), we suppose he made the same du`aa’ for them.
I don’t understand why some Muslims want to have two moral systems: one for them and one for non-Muslims, and are willing to discriminate against non-Muslims even in praying for healing a sick human being, while the message of the holy Qur’an is universal, and the Prophet (peace and blessings be upon him) was sent as (a mercy to humankind) (Al-Anbiyaa’ 21:107).