A spokeswoman for the Israeli military said on Monday the man had been shot after he tried to attack a soldier with a knife. She did not immediately confirm that the Palestinian had been killed.
"An attacker came and attempted to stab a soldier very close to the Tomb of the Patriarchs," she said. "He failed and they managed to shoot him."
Paramedics initially said the man had died in the shooting, but the Israeli account of events could not be immediately verified.
Al-Haram al-Ibrahimi mosque compound, referred to by Israelis as the Tomb of the Patriarchs, is a religious site sacred to Muslims, Jews and Christians.
Meanwhile, in the southern Gaza Strip, a mortar bomb fired by Palestinian resistance fighters hit an army post but caused no injuries, the Israeli army said.
It was the first such attack since a mortar and rocket barrage on Thursday in the occupied territory.
Thursday's mortar attack was in response to the killing of two Palestinians, Fathi al-Alami, who died in an explosion near his home on Wednesday, and Hasan Abu Jazar, who died after being shot on Wednesday in Rafah.