The army said the shooting at a bus stop near the Ofra settlement also wounded at least two other people, although a spokesperson was unable to confirm reports the assailant targeted Israeli soldiers.
"We are searching for the terrorist. We will find him," the military said on Twitter.
The Israeli army said it responded by encircling the West Bank city of Ramallah and sending in reinforcements.
In a separate attack, an assailant stabbed two Israeli border police in Jerusalem's Old City early on Thursday before being shot dead, in the most turbulent 24 hours in the West Bank and Jerusalem in months.
The West Bank shooting came only hours after Israeli forces killed two Palestinians in the West Bank following attacks that claimed the lives of three Israelis, including a baby.
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One of the two Palestinians was Salah Barghouti, a 29-year-old accused of shooting at Israelis on Sunday, also at a bus stop near the Ofra settlement.
That attack wounded seven people, including a woman who was seven months pregnant.
Doctors tried to save the baby boy with an emergency cesarean but he died on Wednesday and was laid to rest in Jerusalem.
His mother remains in hospital in a serious condition.
The exact details of Barghouti's shooting remained murky, but pictures have circulated online of a taxi with multiple bullet holes north of Ramallah.
The other Palestinian killed by Israeli forces overnight had been suspected of shooting dead two Israelis in October.
Ashraf Naalwa, 23, was killed when forces tried to arrest him near Nablus in the West Bank, the Israeli Shin Bet security service said.
The armed wing of Palestinian Hamas said the two men killed by Israeli forces were its "fighters".
The Israeli raids come just as a deal had been secured to restore relative calm to another part of the Palestinian territories, the Gaza Strip.
Oslo Accords 25 years on: From hope to deadlock in Israel-Palestine peace process
The house near Nablus where Naalwa was found was peppered with bullet holes after the raid, with furniture destroyed, an AFP journalist at the scene said.
Local resident Huwayda Bushkar said she saw Israeli soldiers carrying a body as they left.
On October 7, Naalwa allegedly shot and killed two Israelis, 28-year-old Kim Yehezhel and 35-year-old Ziv Hagbi, in the Barkan industrial zone settlement.
The two were employees of the recycling company where Naalwa worked.
A third incident on Thursday morning saw a man stab two Israeli border police in Jerusalem's Old City before being shot dead.
There were no immediate details on the identity of the assailant.
The violence came amid heightened tensions in the West Bank.
Since Sunday's attack Israeli forces had made a series of incursions into central Ramallah, the home of secular Palestinian president Mahmud Abbas.
In recent days Hebrew posters have been erected in the West Bank encouraging the killing of Abbas.
Palestinian Hamas hailed Sunday's shooting, saying it proved "resistance" was still alive in the West Bank.
Israel seized control of the West Bank and east Jerusalem in a 1967 war.
Around 600,000 Israelis now live in settlements there considered illegal by the international community.
Many Palestinians consider violence against Israelis in the West Bank a justified response to the growth of settlements on land they see as theirs.
Speaking Wednesday evening before Barghouti was killed, Israeli Prime Minister Benjamin Netanyahu vowed those who carried out the drive-by shooting would be found and brought to justice.
"We lost a few hours ago a newborn baby, four days old," Netanyahu said in an address to foreign media.
US peace envoy Jason Greenblatt said in a Twitter message that the baby's death was "absolutely heartbreaking".
"This is an attack Hamas praised as 'heroic,'" he wrote.
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