The question whether nonionizing electromagnetic radiation of low intensity can cause functional effects in biological systems has been a subject of debate for a long time. Whereas the majority of the studies have not demonstrated these effects, some aspects still remain unclear, e.g., whether high-frequency radiation in the terahertz range affects biological systems. In particular for frequencies higher than 0.150 THz, investigations of the ability of radiation to cause genomic damage have not been performed. In the present study, human skin cells were exposed in vitro to terahertz radiation at two specific frequencies: 0.380 and 2.520 THz. Power intensities ranged from 0.03–0.9 mW/cm² and the cells were exposed for 2 and 8 h. Our goal was to investigate whether the irradiation induced genomic damage in the cells. Chromosomal damage was not detected in the different cell types after exposure to radiation of both frequencies. In addition, cell proliferation was quantified and found to be unaffected by the exposure, and there was no increase in DNA damage measured in the comet assay for both frequencies. For all end points, cells treated with chemicals were included as positive controls. These positive control cells clearly showed decreased proliferation and increased genomic damage. The results of the present study are in agreement with findings from other studies investigating DNA damage as a consequence of exposure to the lower frequency range (<0.150 THz) and demonstrate for the first time that at higher frequencies (0.380 and 2.520 THz), nonionizing radiation does not induce genomic damage.