BEIJING—It didn’t take long to identify the suspected source of a deadly coronavirus outbreak in the Chinese city of Wuhan: a cluster of vendors in a downtown market offering carcasses and live specimens of dozens of wild animals—from bamboo rats to ostriches, baby crocodiles and hedgehogs.

The Huanan food market, a scruffy complex of 1,000 stalls spread over an area the size of nine football fields, is the largest of its kind in central China, mostly supplying seafood to Wuhan’s residents and restaurants. It is typical of...