Family members said the incident happened as Mohammed Awwad, 17, was travelling in a car with his 19-year-old brother back to their home in Beit Ummar, between the southern cities of Bethlehem and Hebron.
As the two drove past an army outpost at the entrance to the village, soldiers opened fire, with one bullet hitting Awwad in the head and a second hitting his older brother in the thigh, the family said.
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Both were taken to hospital in Hebron.
A spokeswoman for the army told AFP that soldiers opened fire after a suspected improvised explosive device was thrown at soldiers from a car driving past the Beit Ummar outpost.
The army said forensics experts were still working on determining the exact nature of the device, which did not explode.