Iceland, which ranks number one on the global gender gap index, is co-hosting the event with the South American country of Suriname, which ranks 109.
All five top spots on the index compiled by the World Economic Forum are held by Nordic countries — Finland (2), Norway (3), Sweden (4) and Denmark (5) — while Germany takes the 12th position, followed by France which ranks 18th.
Britain lags behind at 26, below the United States which ranks 20th. Yemen takes the last spot at 142.
Organizers said it was unclear how many countries will be represented at the Barbershop Conference, but the ambassador said there was much enthusiasm at the United Nations surrounding the event.