TOKYO—A prefecture just south of Tokyo said it had detected higher-than-permissible amounts of radioactive material in tea leaves, in a reminder that Japan's radioactive-contamination problems are far from over.

The contamination—the first case in nearly a month that an agricultural product has been found tainted outside Fukushima Daiichi's home prefecture—is also the first time that any agricultural item from Kanagawa Prefecture, which includes Yokohama, was found to contain an excessive level of radioactivity.

Japan...