More than 110 countries, including more than 50 African nations, co-sponsored the resolution in the General Assembly's rights committee, which called on states to "complement punitive measures with awareness-raising and educational activities" to eliminate female genital mutilation.
About 140 million women worldwide are believed to have been subjected to the practice in which a young girl's clitoris and labia are removed, in the belief that this will reduce libido and keep a woman chaste.
About three million women and girls each year are said to be forced to undergo the procedure.
"We will continue to spare no efforts with a final objective: ending female genital mutilations in one generation. Today, this goal appears closer than ever," said Cesare Ragaglini, UN ambassador for Italy, which has played a leading role in international efforts to eradicate the practice.
He called the UN resolution a "powerful tool" against widespread resistance because it would take condemnation and calls for new measures to another level.
"It is up to us now to exploit it in a more effective way," Ragaglini said.