Accumulating somatic mutations have been implicated in age-related cellular degeneration and death. Because of their random nature and low abundance, somatic mutations are difficult to detect except in single cells or clonal cell lineages. Here, we show that in single hepatocytes from human liver, an organ exposed to high levels of genotoxic stress, somatic mutation frequencies are high and increase substantially with age. Considerably lower mutation frequencies were observed in liver stem cells (LSCs) and organoids derived from them. Mutational spectra in hepatocytes showed signatures of oxidative stress that were different in old age and in LSCs. A considerable number of mutations were found in functional parts of the liver genome, suggesting that somatic mutagenesis could causally contribute to the age-related functional decline and increased incidence of disease of human liver. These results underscore the importance of stem cells in maintaining genome sequence integrity in aging somatic tissues.