Unicef, citing contacts in Saudi Arabia on Friday, said more than 50 schools have also been closed in the country, after fighting between Yemeni government forces and Houthi rebels in Yemen's north spilled over into Saudi Arabia last week.
"Unicef is deeply concerned about the escalation of the conflict in northern Yemen," Sigrid Kaag, the Unicef regional director for the Middle East, said in a statement.
"Fighting has now spilled over into Saudi Arabia, reportedly causing 240 villages to be evacuated."
Unicef said thousands of people in Yemen have also fled the fighting, with the number of displaced at a camp in Yemen's Hajjah governorate more than doubling in four weeks to 15,000 people.
"Unicef urges all parties to ensure that children are protected from violence and receive all the assistance they need," Kaag said.
The news came as Saudi Arabia vowed to continue its air and artillery attacks against the rebels as part of efforts to reinforce a 10km-deep buffer zone inside Yemen.
The zone is designed to keep members of the Yemeni rebel group away from Saudi Arabia's southwestern border.The Houthi fighters have accused Saudi Arabia of flying over their territory and firing scores of rockets on villages.
Video footage released by the fighters on Thursday allegedly contains images of Saudi missile attacks in Yemen's northern Saada province.
Hussein Shobokshi, a columnist for the Asharq Al Awsat newspaper in Saudi Arabia, said the latest video release is part of a "propaganda war" by the Houthis.
"The Saudis have stated from day one that they are keen to protect their borders [and] that they are keen to create a buffer zone. These were all public announcements," he told Al Jazeera.
"The activities on the Saudi-Yemeni border by the Saudis have been to clear that area from any insurgencies.
"So the Saudis were doing this to defend their territories and to clear a buffer zone to protect [the country] from future attacks by the Houthis.
"The Saudis have a great interest to protect that border because the Yemeni government has failed to protect that border. The Saudis had no choice but to take this severe and dynamic action against tthe Houthis immediately."
Saudi Arabia launched its offensive against the Houthis, who are named after their deceased former leader, after they apparently crossed the border and seized control of a small area.
The Houthis say that the Saudis have been allowing Yemeni troops to use the area to attack their positions.
But a Saudi government adviser said that there were no Saudi troops fighting on the ground inside Yemen, where the terrain is too mountainous to deploy tanks and artillery effectively.