There were conflicting reports about the boy's age, with some reports saying he was 11 and others 13.
In the West Bank raid, neighbours said the boy was inside the house at the time of the shooting and was hit in the crossfire.
Relatives of the boy said he lived in Israel with his parents, and that his mother is a divorced Palestinian woman who is now married to an Arab-Israeli.
The raid was carried out to arrest Islamic Jihad fighters, the military said.
An army spokeswoman said Israeli forces found two Kalashnikov rifles, military vests and ammunition during the West Bank raid.
The military also said that an Israeli paramilitary policeman was wounded and treated at the scene.
The Israeli army said it was investigating whether the Israeli boy was killed by Palestinian or Israeli fire, the Israeli Haaretz newspaper reported.