An army statement said a vehicle approached Israeli soldiers in a suspicious manner near the Jewish settlement of Halamish and the Palestinian village of Nabi Saleh.
"The soldiers perceived the vehicle as a threat and consequently fired towards it in order to stop it," it said.
The Palestinian health ministry said one man died, identifying him as 26-year-old Mohammed Mussa.
A health ministry spokesman told AFP the man was travelling with his sister when they were shot.
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Israel's military said no soldiers were wounded and "the event is being reviewed".
A wave of unrest that erupted in October 2015 has claimed the lives of at least 303 Palestinians or Arab Israelis, 51 Israelis, two Americans, two Jordanians, an Eritrean, a Sudanese and a Briton, according to an AFP toll.
Israeli authorities say most of the Palestinians killed were carrying out knife, gun or car-ramming attacks.
Others were shot dead in protests and clashes, while some were killed in Israeli air strikes on the Gaza Strip.