Israel's Zaka rescue service, which monitors army communications in the occupied West Bank, said the dead child was aged nine.
"An Israeli patrol noticed two figures placing a suspicious object on the road," the spokeswoman said.
"The force called on them to identify themselves. They did not. The patrol then fired in the air and then at one of the figures, and saw he was hit."
An army doctor pronounced the Palestinian dead at the scene. The spokeswoman described him as a youth but said she did not know his age. She said the second Palestinian escaped.
Israel's Haaretz newspaper said it appeared that two children had been building a stone barrier across the road, near the Jewish settlement of Shilo.
"We are checking the circumstances [of the shooting]," the spokeswoman said. She said that it was not immediately clear exactly what the two Palestinians had placed on the road.