The evil eye may be given by the kaafirs

Yes, the evil eye may be given by a kaafir. The evidence for that is the aayah (interpretation of the meaning):

 “And verily, those who disbelieve would almost make you slip with their eyes (through hatred) when they hear the Reminder (the Quran)…” [al-Qalam 68:51]

 Al-Saddi said: “[This means] they would harm you with their eyes (evil eye).” Tafseer al-Baghawi, 8/202.

 This is also indicated by the general meaning of the words of the Prophet (peace and blessings of Allah be upon him): “The (evil) eye is real.” Narrated by al-Bukhari, 5740; Muslim, 2187.