A Reuters photographer at a checkpoint near Tayasir, in the Jordan Valley, saw three bodies being taken from the scene in an ambulance and Israeli media reported that at least 10 people had been wounded.
The online Ynet outlet reported that the attacker, armed with an M-16 automatic rifle, opened fire from close range on a soldier coming out of a fortified bunker, leading to a gunfight that lasted several minutes.
The Israeli military confirmed the attack had taken place but gave no immediate details.
The incident occurred during a period of heightened tension in the West Bank, with major Israeli operations underway in the cities of Jenin and Tulkarm and smaller scale incidents in other locations.
Thousands of Palestinians left their homes in Jenin after Israel told them to go, through drones with loudspeakers. After destroying roadways and other infrastructure, Israeli forces demolished multiple buildings at the weekend, causing loud explosions.
Residents trudged away along rubble-strewn roadways to an assembly point where Red Crescent vehicles awaited.
UNRWA, the UN Palestinian relief agency, said the demolitions in Jenin "undermine the fragile ceasefire reached in Gaza, and risk a new escalation".
It said Jenin, a township for descendants of Palestinians who fled or were driven from their homes during the 1948 war around the creation of the state of Israel, "has been rendered a ghost town".
The refugee camp, long a stronghold of militant groups, has been raided repeatedly over the years - not only by Israel's military but also by the Palestinian Administration.
Jenin governor Kamal Abu al-Rub said the latest operation had left in the camp only about 100 people from the 3,490 families that had been there before it.
At the start of the Jenin operation, Defence Minister Israel Katz said the army would apply lessons learned in the war in Gaza, more than 100 km to the south.
Seventy Palestinians have been killed in the West Bank this year, including 38 in Jenin, the health ministry said.
Israeli officials say the West Bank is part of a multi-front campaign waged by Iran against Israel through proxies such as Hamas in Gaza and Hezbollah in southern Lebanon, and had long said Jenin risked becoming a "mini-Gaza".
Palestinians see Israel's operation as an attempt to displace Palestinians from land they see as the core of a future state.
Nabil Abu Rudeineh, spokesperson for the Palestinian presidency, called the operation part of a wider effort aimed at "displacing citizens and ethnic cleansing" that had gained new focus since US President Donald Trump - who was due to meet Israeli Prime Minister Benjamin Netanyahu on Tuesday - suggested Egypt and Jordan should take in Palestinians.
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