The soldiers believed the men had intended to throw the bombs at Israeli cars on a road by the nearby Jewish settlement of Bet El.
The shooting comes amid tensions between Arabs and Jews in the Israeli city of Acre during Yom Kippur, a Jewish holiday period.
Friction between Palestinians and Jewish settlers in the West Bank has risen over the last few weeks.
Israel has been urged by the US to dismantle illegal settlements in the occupied West Bank and remove about 500,000 Israelis living there.
Palestinians say that the illegal settlements in occupied territory are a major stumbling block to a peace deal with Israel.