Asifi, a 49-year-old teacher who fled from Afghanistan with her family in 1992, was given the prestigious award for "her brave and tireless dedication to education for Afghan refugee girls," UNHCR said in a statement.
Before she arrived in the Kot Chandana refugee village in Mianwali in northern Pakistan, strict cultural traditions had kept most girls at home, but Asifi slowly managed to convince the community to allow her to teach them.
She initially began teaching a handful of girls in a tent, copying out worksheets by hand.
"When you have mothers who are educated, you will almost certainly have future generations who are educated," Asifi said in the statement.
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"So if you educate girls, you educate generations," she said, adding: "I wish for the day when people will remember Afghanistan not for war but for its standard of education."
Afghanistan represents one of the largest and most protracted refugee crisis in the world, with over 2.6 million Afghans currently living in exile -- more than half of them children, according to UN numbers.
And for Afghan refugee children in Pakistan the numbers are even more dire, with around 80 percent of them out of school, UNHCR said.
"Access to quality and safe education helps children grow into adults who go on to secure jobs, start businesses and help build their communities, and it makes them less vulnerable to exploitation and abuse," UN refugee chief Antonio Guterres said in the statement.
"People like Aqeela Asifi understand that today's refugee children will determine the future of their countries, and the future of the world," he said.
Asifi will receive her commemorative medal and USD 100,000 (88,500 euros) in prize money -- to use to fund a project that compliments her existing work -- at a ceremony in Geneva on October 5.