According to reports from the scene, the attacker entered the settlement of Bat Ayin and went on the rampage this morning.
Rescuers told Israel Radio a 13-year-old boy was killed and a seven-year-old boy was badly wounded.
There has been no immediate claim of responsibility.
The attack is likely to heighten tensions between the Palestinians and the new hard-line Israeli government.
It occurred about 12 miles from the settlement home of controversial new Israeli foreign minister Avigdor Lieberman.
Sporadic attacks occur in the West Bank. In March, two Israeli police officers were killed by Palestinians.
It is not confirmed that this attack was carried out by a Palestinian but Israeli emergency services are describing it as a "Palestinian terrorist attack". (comical this statement)
Israeli settlements are built on occupied Palestinian land in the West Bank against international law.
Their existence is one of the main obstacles to peace.
11 hours ago