A student at the school in Jaba, a village outside Jenin, was playing with an explosive device before it detonated, police said. The student found it outside the school and brought it to the classroom, said Haider Ershade, Jenin's mayor.
The Israeli army said it had no troops in the area, which is under Palestinian control, but its forces have patrolled the village searching for militants.
Palestinian police checked the shrapnel found at the scene and said the device was Israeli-made, Ershade said.
Israeli police said a Jewish extremist group calling itself the "Revenge of the Infants" claimed responsibility for the bombing, but police doubted the veracity of that claim.
"We have no investigative evidence to support this claim," police said.
An Israeli army spokesman said on condition of anonymity that the army rarely conducts extensive military operations in Jaba and he doubted soldiers would have left an explosive device.
Meanwhile, clashes between Israeli troops and Palestinians on Wednesday killed at least three people, including a 16-year-old boy, as thousands poured into the streets to mourn seven killed in a missile strike the night before.
The U.S. "roadmap" for Middle East peace is already developing a few detours.
At their news conference in Northern Ireland this week, President Bush and British Prime Minister Tony Blair vowed to press on toward for peace between Israel and the Palestinians.
Publicly, Israeli officials say they're ready to work with Mr. Bush to implement the roadmap, but privately there's growing concern in Jerusalem about the linkage between Iraq and the Israeli-Palestinian conflict, reports CBS News Correspondent Robert Berger.
Israel fears that Britain, which is seen as pro-Arab, is pushing Mr. Bush to force Israel into dangerous concessions. Officials say the U.S. wants those concessions to appease Arab anger over the war in Iraq.
Also, the Palestinian prime minister-designate is running into obstacles from Yasser Arafat in trying to put together a new Cabinet. The disputes could delay publication of the U.S.-backed Mideast peace plan, and Mr. Bush is showing some impatience.
Palestinian sources say Arafat is trying to cling to as much power as possible, especially over the security forces.
It appears that Mahmoud Abbas, the Palestinian prime minister-designate, will not present his Cabinet on schedule Thursday. Palestinian law allows him to ask for an extra two weeks.
Publication of the peace plan depends on Abbas assuming power. The plan, sponsored by the United States, Europe, Russia and the United Nations, is known commonly as the "road map" and calls for Palestinian statehood in 2005 at the end of a three-phase process.
The plan was delayed first by Israel's elections in January and then by the process of appointing the Palestinian prime minister. Speaking in Belfast, Northern Ireland on Tuesday after meeting Blair, Mr. Bush hinted at impatience.
"I look forward to him (Abbas) finally putting his Cabinet in place so we can release the road map," he said.
Arafat grudgingly appointed Abbas, his longtime PLO deputy, as premier, giving in to intense international and domestic pressure to reform his corruption-plagued regime.
Israel and the United States had declared a boycott of Arafat, charging that he was implicated in terrorism. Both hoped that the appointment of Abbas would signal that Arafat was turning over significant power, allowing Abbas to run daily affairs and security and have a hand in peace negotiations.
But Palestinian officials and Western diplomats, speaking on condition of anonymity, said that instead, Arafat is raising obstacles and trying to cling to as much power as possible.
Using his Fatah movement as a base, Arafat is trying to override Abbas' intention to replace most of the Cabinet, turning out veteran politicians and Arafat aides.
Violence is also picking up again. A top Islamic militant was killed Tuesday in the first Israeli air strike since the war in Iraq began.
A warplane and helicopter blasted a car with missiles in Gaza City, killing Saed Arabeed and another Hamas militant, as well as five bystanders. Israel says Arabeed was responsible for dozens of deadly attacks and suicide bombings over the past nine years.
The killing of Arabeed was followed by a string of attacks. Hamas militants retaliated by shooting a rocket at the Israeli town of Sderot on Wednesday, and Israeli troops said they opened fire on another group of Palestinians approaching a rocket launcher. Doctors said two farmers were wounded by gunfire.