The 13-year-old, Abdel Rahman Shadi, died after being hit by a live bullet to the chest while another Palestinian protester was wounded in clashes that took place at Rachel's Tomb in Bethlehem, according to a doctor at the Beit Jala hospital.
The Israeli military confirmed troops opened fire, and said it was investigating further.
Earlier Monday, an 18-year-old Palestinian was killed in clashes in the northern West Bank town of Tulkarem, according to a doctor there. Both doctors spoke on condition of anonymity because they were not authorized to talk to the media.
The latest surge of violence comes at a time when most Palestinians no longer believe in the possibility of statehood through negotiations with Israel. At the same time, Palestinian President Mahmoud Abbas has not charted an alternative path to independence.
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Gaps remain vast between him and Israeli Prime Minister Benjamin Netanyahu on the ground rules of negotiations, and the two have been trading blame.
On Sunday, the Israeli government to take unprecedented security measures. As of Sunday, it barred Palestinian residents of Jerusalem from entering the Old City for two days during a Jewish holiday, in an attempt to curb Palestinian attacks. Palestinians who live, work and study within the Old City, as well as Israelis and tourists, are allowed in.
Israeli police said Palestinians threw rocks and firebombs in mostly Arab areas of Jerusalem in the night from Sunday to Monday. The Palestinian Red Crescent said over 450 Palestinians were injured in the violent protests over the last two days.