Tostan has encouraged thousands of women to speak out against female genital cutting, a taboo subject in Muslim communities of West Africa.
Amartya Sen, a Nobel Prize-winning economist and a Hilton Prize juror, said: "There are many great things about Tostan and its leadership but the most important is (Melching's) freshness of approach and ability to think differently.
"She has put new thought into the discussion about how you get a critical proportion of the population to agree and act in unison, to be an example to others."
Tostan's grassroots approach, using indigenous African languages and working in the poorest communities, has drawn comparisons with the campaign against foot-binding in China.
About 10 years ago, the women of Malicounda Bambara, a village south of Senegal's capital Dakar where Tostan is active, had publicly abandoned female genital cutting and they were the first community in the region to do so.
Neighbouring villages had joined the initiative, despite the risk of leaving the village ostracised as its women were no longer deemed fit to marry, and potential husbands had looked elsewhere.
Today, nearly half of Senegalese villages have made similar declarations, along with 298 in Guinea and 23 in Burkina Faso.
Melching had founded Tostan after setting up a centre in Dakar to educate street children using language and culture familiar to them.
She said: "We started realising how important it was to use the traditional means of communication that people have here in Africa in order to teach.
"We really researched traditional games, stories and songs used at ceremonies like marriages and baptisms. There were songs the women sang when they were harvesting millet. Or if they went to the well."
Melching will travel to New York in September to receive the award at a ceremony due to be attended by Ban Ki-moon, the UN secretary-general.
Tostan now runs Community Empowerment Programmes using the same techniques to teach about everything from forced marriage to microfinance, in hundreds of villages in Senegal, Guinea, Gambia, Mauritania and Somalia.
It will soon also start in Djibouti.
Tostan was one of nearly 250 nominees for the Hilton Prize, awarded each year since 1996 by the Conrad N Hilton Foundation.