Israeli military sources said the clash broke out in the Tel Rumeida neighbourhood, which is home to radical Jewish settlers, on Wednesday.
The sources orginally said two soldiers had been lightly wounded in the incident, but later reported it was two armed settlers instead.
They added the Palestinian man opened fire at an army patrol before being gunned down by settlers in the vicinity.
The slain man, who was named by witnesses and his family as Rafiq Nabih, was 23 years old.
Jewish settlers are protected by
hundreds of Israeli soldiers
During the afternoon, Israeli troops came to Nabih's house and arrested his father, Ziad, and brother-in-law Amjad Zahadi, witnesses said.
The family was staying inside the house for fear the army would destroy it.
Under the terms of an agreement with the Palestinian Authority, Israel withdrew from 80% of Hebron in 1997, but continues to occupy an enclave near the Tomb of the Patriarchs.
Within the enclave live 600 hardline settlers who are protected by hundreds of soldiers and surrounded by 120,000 Palestinians.
Meanwhile, at least three Palestinians were reported to be in a critical condition when their car was destroyed in a violent explosion in Nablus on Wednesday evening.
Palestinian security sources said it was not immediately clear what had caused the explosion, which took place in the eastern part of the city shortly after 20:00 GMT.
The violence comes a day after a Palestinian man was shot and killed by Israeli soldiers during a raid into the West Bank city of Ram Allah.
Another eight Palestinians were wounded when about 40 Israeli army jeeps and armoured trucks stormed the city on Tuesday evening.