Fallout with rain from the Fukushima reactor accident was monitored for about two months in Higashi-Hiroshima City, Hiroshima, Japan, from March 20 to May 23, 2011. Gamma-ray (γ-ray) spectra measured using a low background HPGe spectrometer showed clear evidence of fission products—131I, 137Cs, and 134Cs. The 131I was observed on March 27 and April 8, while 137Cs and 134Cs were observed on March 27, April 18, and April 22. The 131I, 137Cs, and 134Cs activity concentrations in rainwater collected in Hiroshima reached 0.44 ± 0.09 on April 8, 0.17 ± 0.01 on April 18, and 0.15 ± 0.01 Bq/L on April 18, 2011, respectively. These activity levels were compared with global results collected from the Northern Hemisphere. Several samples of rainwater that were collected in Chiba (Kashiwa) on March 21, April 11, and May 12; Tokyo (Nerima) on March 21 and April 11; Osaka (Hirano) on April 8; Nara (Kitakatsuragi) on April 9; and Fukushima (Fukushima) on April 19, were also measured by our spectrometer and compared. Among these samples of rainwater collected at different locations in Japan, the one collected at Kashiwa City, Chiba Prefecture, on March 21 showed the highest activity concentrations of 6072 ± 1, 632 ± 4, 766 ± 3, 637 ± 1, 97.6 ± 0.8, and 752 ± 2 Bq/L for 131I, 132I, 132Te, 134Cs, 136Cs, and 137Cs, respectively. The health risks due to these high activity levels were considered in terms of several regulations. The ratio of the activites for the isotopes 131I to 137Cs and 134Cs to 137Cs were compared with the other measurements and discussed.