Live updates: Follow the latest on Israel-Gaza
The death toll continued to rise on Thursday evening, hours after the Israeli army entered the tightly packed camp, which has been a regular site of military raids in recent months.
Four others were killed in separate incidents near Bethlehem, Hebron, Nablus and Ramallah.
It is the biggest operation in the camp since July, when more than a dozen people were killed in a raid that reduced much of the refugee camp to rubble.
Almost 180 people have been killed across the West Bank since October 7, accounting for more than half of all deaths this year.
Israel says most of the dead are militants, including Hamas operatives, either responsible for or planning attacks on Israelis, dozens of whom were killed in a spate of Palestinian attacks over the past year.
Children and the elderly have also been killed by the army, including a 15-year-old who died in the Thursday raid on Jenin.
The army said it was aiming for militants who had hidden bombs and weapons inside the camp.
It has increased raids into the West Bank since Hamas militants killed about 1,400 people in the worst attack in Israel's history on October 7, prompting air strikes and ground incursions on Gaza that have left more than 10,800 dead.
At least 4,300 schoolchildren were trapped in their schools as Thursday's raid progressed, education officials told the official Wafa news agency.
Some were later moved to a nearby stadium, while a number of nursery pupils were taken to hospital "to check on their condition and calm them psychologically".
Troops surrounded Jenin's government hospital, Wafa said.
It said the army raided the emergency department and shot at ambulances.
The Palestinian Red Crescent said one of its ambulances came under fire, stopping medical teams reaching an injured person.
At least 2,000 people have been arrested across the West Bank in the past month, including workers from Gaza, according to Palestinian officials.
Rising settler attacks on civilians have also ignited concern among critics and allies of Israel, including the US.
US President Joe Biden has said settler attacks on Palestinians "must stop," and Washington has instructed the Israeli government to take action against Israelis attacking Palestinians in the occupied West Bank.
At least nine Palestinians have been killed in such attacks since October 7, according to authorities.
Many more have been forced to leave their homes, as seen in the Hebron Hills area, where residents told The National they were warned to leave or be killed