The shooting took place after Israeli troops took over homes in the town of Jenin where a group of gunmen was hiding, taking up position and fighting them.
Palestinian witnesses said the soldiers had usef loudspeakers to call to the armed group to surrender.
The Israeli army said an exchange of fire ensued, in which the soldier was killed.
One Palestinian came running out early on in the gun battle, and four others surrendered later, it said.
Palestinian gunmen took to the streets immediately after the houses were surrounded, exchanging fire with troops.
Palestinian students threw stones at Israeli soldiers, and an army bulldozer tried to disperse the crowd.
The five men were said to belong to Islamic Jihad and the Al Aqsa Martyrs' Brigades, a group with ties to the Fatah movement.
Earlier on Thursday, Palestinian gunmen shot and wounded two Israeli motorists near a Jewish settlement in the northern West Bank.
The Israelis were taken to hospital with light to moderate wounds, the army said.
The Jenin operation comes two days after the army conducted a prison raid in the West Bank town of Jericho, spiriting away six prisoners, including Ahmed Saadat, a leader of the People's Front for the Liberation of Palestine.