Majdi Qullab, 21, was in critical condition after being hit in the stomach, arm and leg by live gunfire, the sources said. Another youth was in moderate condition after being hit by rubber bullets, they added.
The shooting happened near the city's old quarter, the scene of repeated search operations by the Israeli military.
Also on Friday an explosive device was detonated next to an Israeli jeep in the eastern part of Nablus, but caused no casualties, an Israeli army spokesman said.
Palestinian security sources and witnesses said the blast damaged an army jeep driving some 300 metres (yards) from Joseph's Tomb, a shrine considered as the resting tomb of the Biblical patriarch.
An Israeli army spokesman confirmed that an explosive device had been detonated near troops in eastern Nablus, but said it had caused no injuries or damage.
The city has been under curfew for the past eight days as troops have been searching for wanted activists.