The hospital's X-ray machine is broken, but Atar and his team perform nearly 60 surgeries per week in a room with just one light, with staff using "ketamine injections and spinal epidurals" instead of general anesthesia, the agency said.
UNHCR chief Filippo Grandi said Atar's "profound humanity and selflessness" had saved thousands of lives.
Khartoum unilaterally announced a ceasefire in the area in March.
Last year's winner was Nigerian Zannah Mustapha, who helped negotiate the release of some of the girls kidnapped by Boko Haram Islamists from their school in Chibok in 2014.
UNHCR said actor and goodwill ambassador Cate Blanchet will deliver the keynote address at the ceremony in Geneva next week.