TOKYO—When Masayoshi Son heard about the nuclear meltdowns in Fukushima last year, he had a mini meltdown of his own.

The chief executive of telecommunications and Internet company Softbank Corp.—these days best known as the man who brought Apple Inc.'s iPhone to Japan—says he told his board he was so concerned by the accident that he couldn't concentrate on his job anymore. Mr. Son said he planned to quit and work on energy issues instead.

"We...