UNRWA says Malala is donating all of the proceeds of the $50,000 World Children's Prize, which she collected in Stockholm on Wednesday.
The agency quoted Malala as saying Palestinian children deserve a quality education, and that "without education, there will never be peace."
Dozens of Gaza's UN schools were damaged or destroyed during the 50-day war. Israel says it fired near schools responding to Hamas' attacks from the areas.
The 17-year-old Malala won this year's Nobel Peace Prize for promoting girls' rights in her native Pakistan. She survived a shot in the head by a Taliban gunman two years ago. AP