Amid the wave of hype over artificial intelligence, a growing chorus of fear has sprung around software engineering, where executives are threatening to automate swaths of work. But an ongoing overhaul at America’s second-largest private employer has a more immediate warning — already on warehouse floors.

Amazon.com Inc. plans to replace more than half-a-million jobs in the United States with robots, the New York Times reported citing internal strategy documents and interviews with executives, as Ameri...