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 the 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.
"The orders are not to go physically into Yemeni territory," he said.
"We don't want to get bogged down there or inflame any local sensitivities, if there are any, against us."
Prince Khaled bin Sultan, the Saudi deputy defence minister, said the offensive would continue until the Houthis "withdraw dozens of kilometres" from the border.
Riyadh has become increasingly anxious about the stability of the government in Yemen, which is facing opposition from the Shia population in the north, separatist sentiment in the south and a growing threat from al-Qaeda fighters.
The Houthis first took up arms against the government of Ali Abdullah Saleh, Yemen's president, in 2004, citing political, economic and religious marginalisation by the Saudi and Western-backed administration.
The conflict intensified in August when Yemen's army launched Operation Scorched Earth in an attempt to crush the fighters in the northern province of Saada.
Aid groups, which have limited access to the northern provinces, say at least 150,000 people are believed to have fled their homes since 2004.
The United Nations refugee agency said last week it was looking into whether the Saudi air raids had affected 3,500 to 4,500 displaced people gathered near the border.