Mutation rates along the genome are highly variable and influenced by several chromatin features. Here, we addressed how nucleosomes, the most pervasive chromatin structure in eukaryotes, affect the generation of mutations. We discovered that within nucleosomes, the somatic mutation rate across several tumor cohorts exhibits a strong 10 base pair (bp) periodicity. This periodic pattern tracks the alternation of the DNA minor groove facing toward and away from the histones. The strength and phase of the mutation rate periodicity are determined by the mutational processes active in tumors. We uncovered similar periodic patterns in the genetic variation among human and Arabidopsis populations, also detectable in their divergence from close species, indicating that the same principles underlie germline and somatic mutation rates. We propose that differential DNA damage and repair processes dependent on the minor groove orientation in nucleosome-bound DNA contribute to the 10-bp periodicity in AT/CG content in eukaryotic genomes. Display omitted •Somatic and germline mutation rates show a 10-bp periodicity in nucleosome-occupied DNA•This periodicity tracks DNA minor groove facing toward and away from the histones•The orientation of the periodicity depends on the mutational processes active in the tissue•This has contributed to the AT/CG 10-bp periodicity in eukaryotic genomes The pattern of exposure of the minor groove of the DNA wrapped around nucleosomes determines a periodicity of the somatic and germline mutation rate, providing broad insights into the human cancer mutational landscape and eukaryotic genome evolution.