Pakistani education activist
The 17-year-old also hit out at world leaders, imploring them to stop creating war and instead use their resources to end conflict.
"This award is not just for me. It is for those forgotten children who want education. It is for those frightened children who want peace. It is for those voiceless children who want change," she said. "I am here to stand up for their rights to raise their voice."
Malala became the youngest ever recipient of the Peace Prize during a lavish ceremony in Oslo attended by dignitaries including King Harald V of Norway. She was jointly awarded the prestigious prize along with Indian child rights campaigner Kailash Satyarthi after the Norwegian Nobel committee recognized her "heroic struggle" for girls' right to education.
Malala received two standing ovations -- at the beginning and end of her address -- as well as several rounds of sustained applause.
"Why is it that countries which we call strong are so powerful in creating wars but are so weak in bringing peace?" she asked. "Why is it that giving guns is so easy, but giving books is so hard? Why is it that making tanks is so easy, but building schools is so hard?"
Malala was shot in the head by Taliban gunmen in October 2012 for campaigning for girls' education. She now lives in Britain.
The teenager said she brought several "sisters" to the ceremony with her, including two classmates who were shot alongside her.
"I tell my story not because it is unique, but because it is not," she said. "It is the story of many girls."
The speech contained some lighter moments, including when she admitted that as much as she was calling for peace globally, this has been harder to achieve at home.
"I'm pretty certain that I'm also the first recipient of the Nobel Peace Prize who still fights with her younger brothers," she said as the audience chuckled. "I want there to be peace everywhere, but my brothers and I are still working on that."
Malala's parents beamed with pride as they watched their daughter speak and she thanked them for their unconditional love and support.
She gave an insight into events that propelled her into the spotlight, detailing how when she was 10 her hometown in Pakistan's Swat Valley suddenly became a place where "dreams turned into nightmares" when more than 400 schools were destroyed.
"Women were flogged, people were killed," she explained. "Education went from being a right to being a crime."
"When my world suddenly changed, my priorities changed too," she added. "I had two options. One was to remain silent and wait to be killed. And the second was to speak up and then be killed. I chose the second one; I decided to speak up."
She said that while she may be small in stature, her campaign could not be dismissed lightly.
"Though I appear as one girl, one person, who is 5-foot-2-inches tall, if you include my high heels. I'm not a lone voice," she said. "I am those 66 million girls who are deprived of education and today I'm not raising my voice, it is the voice of those 66 million girls."
She urged world leaders to make education their top priority and said the money from her prize will go to the Malala Fund to build schools in Pakistan. This is where she will begin, she added, but by no means where she intends to stop.
"We are living in the modern age and we believe that nothing is impossible. We have reached the moon 45 years ago, and maybe we will soon land on Mars. Then, in this 21st century we must be able to give every child quality education."