ADDIS ABABA, Ethiopia—At the Radisson Blu hotel here last year, a senior fashion executive met with several of his top Asian apparel suppliers. His plea: Open for business in Africa.

“Africa is a huge opportunity to demonstrate how the industry can work together,” said Colin Browne, managing director of product supply and Asian sourcing for VF Corp., which owns such brands as Lee, Wrangler and Timberland. He pointed out to the factory owners a key advantage in Africa: it’s one of the few places where it’s possible to go from...