The Palestinian mainstream Fatah group identified the man as Alaa Odeh, a 30-year-old mobile phone shop owner, and along with relatives accused soldiers of killing him in cold blood.
In a statement, the military said "a Palestinian gunman opened fire and wounded a border policemen, and the force returned fire, killing the perpetrator".
It posted on Twitter a photograph of a pistol on the ground and said the attacker had fired six shots.
Odeh's family was quoted as saying in media reports that he was at the checkpoint awaiting a delivery of phones.
The night-time incident came hours after Palestinian President Mahmoud Abbas swore in a new unity government, healing a rift with Hamas Islamists in Gaza, and raising tensions with Israel.
The shooting occurred at the same checkpoint where troops, four days ago, arrested a Palestinian who the military said was wearing an explosives belt.
US-led peace talks between the Israelis and Palestinians collapsed in April and some analysts have warned of a possible spike in violence given the lack of any clear way forward to resolve the generations-old conflict.
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