The platypus is an egg-laying mammal which, alongside the echidna, occupies a unique place in the mammalian phylogenetic tree. Despite widespread interest in its unusual biology, little is known about its population structure or recent evolutionary history. To provide new insights into the dispersal and demographic history of this iconic species, we sequenced the genomes of 57 platypuses from across the whole species range in eastern mainland Australia and Tasmania. Using a highly improved reference genome, we called over 6.7 M SNPs, providing an informative genetic data set for population analyses. Our results show very strong population structure in the platypus, with our sampling locations corresponding to discrete groupings between which there is no evidence for recent gene flow. Genome-wide data allowed us to establish that 28 of the 57 sampled individuals had at least a third-degree relative among other samples from the same river, often taken at different times. Taking advantage of a sampled family quartet, we estimated the de novo mutation rate in the platypus at 7.0 × 10-9/bp/generation (95% CI 4.1 × 10-9-1.2 × 10-8/bp/generation). We estimated effective population sizes of ancestral populations and haplotype sharing between current groupings, and found evidence for bottlenecks and long-term population decline in multiple regions, and early divergence between populations in different regions. This study demonstrates the power of whole-genome sequencing for studying natural populations of an evolutionarily important species.