TOKYO — Some shops in Tokyo began rationing goods — milk, toilet paper, rice and water — as a run on bottled water coupled with delivery disruptions left shelves bare today nearly two weeks after a devastating earthquake and tsunami.

The unusual sights of scarcity in one of the world’s richest, most modern capitals came a day after city officials reported that radioactive iodine in Tokyo’s tap water measured more than twice the level considered safe for babies.

Radiation has been leaking from a nuclear plant 140 miles northeast of Tokyo since it was slammed by the March 11 quake and engulfed by the ensuing tsunami. Feverish efforts to get the plant’s crucial cooling system back in operation have been beset by explosions, fires and radiation scares.

Today, two workers at the Fukushima Dai-ichi plant were treated at a hospital after stepping in contaminated water while laying electrical cables in one unit, nuclear and government officials said. The water seeped over the top of their boots and onto their legs, said Takashi Kurita, spokesman for plant owner Tokyo Electric Power Co.

The two workers likely suffered “beta ray burns,” Tokyo Electric officials said. They tested at radiation levels between 170 to 180 millisieverts, below the maximum 250 millisieverts allowed for workers.