The group says over 1,000 children have been injured since March 30th
UNICEF and its partners have delivered two truck-loads of medical supplies to the Gaza Strip.
The group says this is enough to meet the needs of an estimated 70,000 people.
The drugs and medical equipment include antibiotics, saline solution and syringes for the treatment of injuries.
UNICEF says since March 30th, over 1,000 children were injured in violence in the Gaza Strip.
"Many of these injuries are severe and potentially life-altering, including amputations", it says.
"Recent violence has exacerbated the already weak health system in the Gaza Strip which is crumbling because of severe power cuts and shortages of fuel, medicine and equipment.
"Medical facilities are buckling under the strain of additional casualties wounded in the recent violence, many with complex and life-threatening injuries.
"The intensifying violence has worsened the plight of children whose lives have already been unbearably difficult for many years."
UNICEF Ireland executive director Peter Power says: "I have been to Gaza with UNICEF and I have seen for myself the appalling conditions that children are living in.
"Three wars in 10 years have caused the destruction of basic health facilities, of schools, of family homes and of the basic services children are entitled to. This is the very last thing they need.
"One of the most basic rules in war is the protection of children.
"That norm is being disregarded, with children living out their lives on the very front line of attacks. Enough is enough. Stop attacks on children."
UNICEF's regional director for the Middle East and North Africa, Geert Cappelaere, adds: "The escalating violence in Gaza has exacerbated the suffering of children whose lives have already been unbearably difficult for several years.
"Half of all children depend on humanitarian assistance, and one in four needs psychosocial care.
"In addition to physical injuries, children are showing signs of severe distress and trauma.
"Power cuts and shortages of fuel, medicine and equipment are straining an already fragile health system and complicating access to treatment for the injured.
"Schools are overcrowded and operating on triple shifts, limiting children's learning prospects.
"The minimal power supply in Gaza has disrupted water and sanitation services, severely reducing the availability of drinking water - nine out of 10 families do not have regular access to safe water."
It comes as UN human rights expert Michael Lynk has called on the Israeli government to "immediately cease its lethal assault" against protesters at the Gaza fence.
The special rapporteur on the situation of human rights in the Palestinian territory occupied since 1967 said the prosteters "appear to pose no credible threat to Israeli military forces on the Israeli side of the fence."
He has condemned Israel's excessive use of force towards "largely unarmed demonstrators" at the Gaza fence on Monday, which has left 58 Palestinians dead and almost 2,800 wounded.
He said: "This blatant excessive use of force by Israel - an eye for an eyelash - must end, and there must be true accountability for those in military and political command who have ordered or allowed this force to be once again employed at the Gaza fence."