Israeli police said they suspected a Palestinian attack.
No Palestinian group claimed responsibility for the shooting, which took place near the mainly agricultural settlement of Massuah, in an area of the West Bank close to the border with Jordan that is under Israeli security control.
An official from Israel's ambulance service said medics had found a car that had veered off the road and that the two men inside had suffered gunshot wounds.
Earlier this month, a Palestinian bulldozer driver was shot dead after attacking two police officers in their car with his vehicle in Jerusalem road, overturning their car but causing them light injuries.
Last Wednesday, Israeli soldiers shot and killed a Palestinian youth and wounded another after firebombs were thrown at their vehicle in the occupied West Bank.
