Prime Minister Benjamin Netanyahu threatened a major offensive in the occupied territory just days before an Israeli election.
Netanyahu said the military would "destroy" the neighbourhood where the two attackers came from.
The attack near Hebron in the southern West Bank wounded three other soldiers, the Israeli military said in a statement.
It took place amid escalating attacks by Israeli settlers and a broader rise in violence in the territory since the 2023 Hamas-led attacks that plunged the region into war.
Netanyahu, whose right-wing coalition may lose its majority after Tuesday's election, visited the site of the attack and said the military would force Palestinians out of a Hebron neighbourhood from which he said the attackers had emerged.
He likened the tactic to Israel's devastating military assaults on two Palestinian refugee camps in 2025, operations that displaced tens of thousands of Palestinians. Human Rights Watch said those expulsions amounted to war crimes, something Israel rejects.
"That is exactly what we will do here," Netanyahu said.
"We will evacuate the residents, we will go house-to-house, we will also confiscate the weapons there, and all terrorist infrastructures will be dealt with and destroyed."
After Netanyahu's comments, a Reuters reporter saw Israeli bulldozers begin to demolish homes in Hebron near the site of the shooting. Local residents said the homes facing demolition had no connection to the attackers. Israel's military did not immediately respond to a request for comment.
The violence comes ahead of an October 27 Israeli election, with opinion polls showing both Netanyahu and his main competitor, former military chief Gadi Eisenkot, falling short of a majority in parliament.
Netanyahu's government has presided over a rapid expansion of settlements, deemed illegal by UN bodies and most countries, though Israel disputes this.
Militant settlers have stepped up their attacks on Palestinians in recent weeks during the territory's annual olive harvest, killing at least three Palestinians and wounded dozens of others, including journalists, European diplomats and a French mayor.
Palestinian gunmen have also carried out attacks on Israeli soldiers and civilians in recent months. In September, a gunman shot dead an Israeli man at a spring near a West Bank settlement. The suspected gunman was later arrested.
with AP
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