The sources said 14-year-old Laith Khaldi of the Jalazon refugee camp was shot in the chest during clashes with Israeli forces near the Atara checkpoint on Friday evening and died hours later in hospital.
A spokeswoman for the Israeli army told AFP that "a Palestinian suspect hurled a Molotov cocktail at an army post in Bir Zeit. In response to the immediate danger, the soldiers fired toward the assailant, identifying a hit".
Clashes had erupted in the West Bank on Friday after a Palestinian toddler was burnt to death as the result of an arson attack by Israeli settlers.
Earlier on Friday, a Palestinian man was killed and another wounded by Israeli gunfire in the northern Gaza Strip after they approached the border with Israel, a Palestinian medical official told AFP.
Gaza health ministry spokesman Ashraf al-Qudra said 27-year-old Mohammad Al-Masri died of his wounds after being shot near the border fence west of the Beit Lahiya area.
Israel maintains a security buffer zone along the inside of the Gaza border with limited access for farmers, and it is not uncommon for Palestinians to be shot after approaching the fence.