The shooting erupted after some 15 Israeli jeeps and armoured-personnel carriers entered Qabatiya, just south of Jenin, and surrounded the school.
An army spokesman confirmed troops were carrying out searches in the village, but had no information on the clashes or why the school was surrounded.
Also on Saturday two Palestinians were wounded when Israeli occupation soldiers opened fire during a raid in the Balata refugee camp east of Nablus.
The clashes came a day after two 15-year-old Palestinians from Qabatiya were taken for questioning by the army after they opened fire with a home-made rifle on an army base near a Jewish settlement just west of Jenin.
No one was wounded in the shooting. Palestinian sources confirmed the arrests and a spokesman for the Popular Resistance Committees said the pair were members of the group.
An explosion in East Jerusalem on Saturday night which wounded five Palestinians was an accidental gas blast, Israeli police said.
A police spokesman said it was "due to a concentration of gases...and the build-up of gases caused an explosion that damaged several shop.
Medics said five people were injured, three seriously in the explosion in a fruit and vegetable store near the Damascus Gate entrance to the old city.
Meanwhile, the resistance Islamic group Hamas called on all Palestinians collaborating with Israel to turn themselves in and give up all the information they have in exchange for a promise they will not be punished.
"If you give us information ... we promise not to harm you, not to mention your identities because of the threat on your life ... and not to tell any of your families about your bad past," Hamas said in a statement on Saturday.
Hamas is asking collaborators to
turn themselves in
Hamas said those that do not turn themselves will face divine retribution, and it implied it would take violent action against them as well.
Israeli intelligence makes frequent use of Palestinian informants to track and gather information on wanted fighters and Hamas believes informants enabled Israel to assassinate the group's founder, Shaikh Ahmad Yasin, in March and his successor, Abd al-Aziz al-Rantisi, earlier this month.
Since the outbreak of the Al-Aqsa Intifada in 2000, 83 alleged collaborators have been killed by fighters, six died in Palestinian custody and two were sentenced to death and executed, a Palestinian human rights monitor said.
Hamas fighters have not executed collaborators during the current conflict.
The appeal, signed by Hamas' political wing, asked repentant collaborators to talk to their local religious leaders or local fighters and tell them everything they have done.
"Take this opportunity before it ends, before there is not time for regret. If you do not, we swear to God that your shame will be cleansed by blood and your shame will never end," it said.