Cancer genome sequencing has revealed considerable variation in somatic mutation rates across the human genome, with mutation rates elevated in heterochromatic late replicating regions and reduced in early replicating euchromatin. Multiple mechanisms have been suggested to underlie this, but the actual cause is unknown. Here we identify variable DNA mismatch repair (MMR) as the basis of this variation. Analysing ~17 million single-nucleotide variants from the genomes of 652 tumours, we show that regional autosomal mutation rates at megabase resolution are largely stable across cancer types, with differences related to changes in replication timing and gene expression. However, mutations arising after the inactivation of MMR are no longer enriched in late replicating heterochromatin relative to early replicating euchromatin. Thus, differential DNA repair and not differential mutation supply is the primary cause of the large-scale regional mutation rate variation across the human genome.