Nucleosome organization has been suggested to affect local mutation rates in the genome. However, the lack of de novo mutation and high-resolution nucleosome data has limited the investigation of this hypothesis. Additionally, analyses using indirect mutation rate measurements have yielded contradictory and potentially confounding results. Here, we combine data on >300,000 human de novo mutations with high-resolution nucleosome maps and find substantially elevated mutation rates around translationally stable ('strong') nucleosomes. We show that the mutational mechanisms affected by strong nucleosomes are low-fidelity replication, insufficient mismatch repair and increased double-strand breaks. Strong nucleosomes preferentially locate within young SINE/LINE transposons, suggesting that when subject to increased mutation rates, transposons are then more rapidly inactivated. Depletion of strong nucleosomes in older transposons suggests frequent positioning changes during evolution. The findings have important implications for human genetics and genome evolution.