The Palestinian Red Crescent said Mohammed Daraghme, in his early twenties, was killed at around 8:00 am (0600 GMT) at the Hamra checkpoint northeast of Nablus.
Initial media reports said Daraghme had tried to stab soldiers at the checkpoint -- a claim denied by Palestinian sources.
The Israeli military confirmed that Daraghme was not armed with a knife, but said he entered an unauthorised lane in the checkpoint and was believed to have been holding a bottle. "He was holding a glass bottle and the soldiers were probably scared he was going to try to stab them," a military spokeswoman told AFP.
She could not confirm whether the bottle was broken, or if Daraghme had explicitly threatened the soldiers. "He approached them, he was standing a few metres (yards) from them," she said. "They asked him to stop, he didn't answer."
The incident was under investigation, she added, and many details about the incident remained unclear, including how many soldiers opened fire.
Daraghme, from the village of Tubas, north of Nablus, died at the checkpoint after sustaining bullet wounds to his chest, hand and leg, sources at the Tubas hospital where he was taken told AFP. Palestinian security sources said Daraghme was attempting to pass through the checkpoint on his way to work at a West Bank settlement on Sunday morning and got into an altercation with troops when they refused him passage.
No soldiers were wounded in the incident, and the checkpoint was closed afterwards.
Michelle Bubis, a spokeswoman for Israeli human rights group B'tselem, said the details of the incident were still unclear. "We have eyewitness accounts but we're still checking into it. B'tselem demands a military police investigation and is itself checking into the incident," she told AFP.
On Saturday evening, a Palestinian man was arrested by Israeli troops near the settlement of Gush Etzion, south of Bethlehem, after reportedly trying to stab two female soldiers. The Israeli military said no one was injured in that incident.
Sunday's incident came less than 48 hours after the death of Jawaher Abu Rahma, a 36-year-old Palestinian woman who died after inhaling massive amounts of tear gas fired by the Israeli military at a West Bank demonstration.
Abu Rahma died in hospital overnight on Friday in the West Bank city of Ramallah after collapsing during a protest against the Israeli separation barrier in the nearby village of Bilin, hospital staff said.
The Israeli army said that an "investigation has been opened to determine the exact cause of death," and that it had "unsuccessfully contacted the Palestinian Authority to obtain a medical report." Palestinian chief negotiator Saeb Erakat on Saturday condemned Abu Rahma's death as an "Israeli war crime."