NAMIE, Japan—Fukushima prefecture, a place synonymous in many minds with nuclear meltdown, is trying to reinvent itself as a hub for renewable energy.

One symbol is just outside Namie, less than five miles from the nuclear-power plant devastated by an earthquake and tsunami in 2011. At the end of a winding road through miles of barren land, construction is nearing completion on one of the world’s largest hydrogen plants.

The...