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 Qur’aan)…”
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 Allaah be upon him): “The (evil) eye is real.” Narrated by al-Bukhaari, 5740; Muslim, 2187.