Hazem Lahliuh, from the village of Arraba, south of Jenin, was wounded after being shot close to the military gate at a separation barrier, which divides Israel and the West Bank.
Red Crescent workers said that he was moved to a hospital in Jenin for treatment.
Alaa Abu Baker, from the village of Qaffin, north of Tulkarem, was also injured near the wall.
The attacks happened in separate incidents of Israeli violence.
Half-a-century of illegal occupation
Israel has occupied the West Bank illegally since 1967, and commits various abuses against Palestinian civilians, human rights groups say.
More than 600,000 Israeli Jewslive in settlements in the occupied West Bank and East Jerusalem, in constructions considered illegal under international law.
The Oslo agreement of 1995 divided the occupied West Bank into three: Area A, Area B and Area C.
Area A is under the administrative and security control of the Palestinian Authority (PA). Area B's administration is controlled by the Palestinian Authority, with Israel controlling security. Area C is under full administrative and security control of Israel.
Along with illegally confiscating Palestinian land, Israeli soldiers and settlers routinely harass Palestinians in the occupied territories in various ways.
Israeli forces and settlers routinely harass local residents in the occupied territories through harming and killing civilians, demolishing homes, poisoning livestock, vandalising property and other forms of violence.
Israel often forces Palestinians to demolish their own homes under the pretext of not having permits to construct the buildings.
Applications for building permits often take years to be processed, giving Israeli courts a loophole to increase Palestinian home demolitions by branding structures as "illegal".