TOKYO—Japan grappled with a fresh radiation scare Tuesday, as authorities found that beef contaminated with radioactive cesium had been shipped to shops and restaurants throughout the country.

The beef, from six cattle raised on a farm near the stricken Fukushima Daiichi nuclear plant, registered radioactive-cesium levels up to seven times that permitted by Japanese food-safety standards. Some of the meat had already likely been eaten, government officials said.

Experts...