The campaign by the UN High Commissioner for Refugees is called ninemillion.org and was unveiled in Washington on World Refugee Day.
The UNHCR plans to allocate two-thirds of private and company donations it receives to finance education projects in refugee camps.
The remaining money will be earmarked for the Canadian humanitarian organisation "Right to Play".
The organisation promotes the development of refugee children, particularly girls, through play and sports.
"Children in refugee camps not only need survival," said US Olympics speed skating champion Joey Cheek.
"They need education, sports, play, all the things that help all of us grow," he said.
UNHCR said on its Internet pledge site that it had registered 20.8 million refugees and people in need of protection around the world, 9.3 million of them children.
The drive is backed by an advertising campaign featuring a 30-second video with Brazilian soccer superstar Ronaldo. There are also short films portraying the lives of young refugees.
The US software giant Microsoft and sports apparel company Nike are the main initial financial backers of the drive.
Nike already has announced the donation of 40,000 green and yellow balls especially designed to survive the tough conditions of refugee camps.