The history of Israel and its creation are unknown, due to the Divergence. However, in the Fallout world before the Great War, the country of Israel was almost certainly a place where Arab-Israeli tensions often boiled over into conflict as in the real world. This seems especially true due to the fact in December of 2053, a terrorist nuclear weapon destroyed Tel Aviv, a large city in the country, irradiating the surrounding area. It is unknown if Israel was destroyed in the attack.
Israel is only mentioned in the Fallout Bible timeline, although weapons made by Israeli companies appear in Fallout, Fallout 2, Fallout Tactics, and Fallout: Brotherhood of Steel. Israel is also referenced in an inscription on a gravestone in Golgotha.