GAROUA, Cameroon—Not long ago, a Dutch neurobiologist announced a surprising discovery: A root used by rural West African healers to treat pain contains an apparently natural version of a man-made opioid.

The root from northern Cameroon had such high levels of a painkiller called tramadol that mice given an extract and placed on a hot plate didn't feel their feet burning at first.

A year later, German rivals came up with a…