Mitochondrial DNA has been heavily utilized in phylogeography studies for several decades. However, underlying patterns of demography and phylogeography may be misrepresented due to coalescence stochasticity, selection, variation in mutation rates and cultural hitchhiking (linkage of genetic variation to culturally‐transmitted traits affecting fitness). Cultural hitchhiking has been suggested as an explanation for low genetic diversity in species with strong social structures, counteracting even high mobility, abundance and limited barriers to dispersal. One such species is the sperm whale, which shows very limited phylogeographic structure and low mtDNA diversity despite a worldwide distribution and large population. Here, we use analyses of 175 globally distributed mitogenomes and three nuclear genomes to evaluate hypotheses of a population bottleneck/expansion vs. a selective sweep due to cultural hitchhiking or selection on mtDNA as the mechanism contributing to low worldwide mitochondrial diversity in sperm whales. In contrast to mtDNA control region (CR) data, mitogenome haplotypes are largely ocean‐specific, with only one of 80 shared between the Atlantic and Pacific. Demographic analyses of nuclear genomes suggest low mtDNA diversity is consistent with a global reduction in population size that ended approximately 125,000 years ago, correlated with the Eemian interglacial. Phylogeographic analysis suggests that extant sperm whales descend from maternal lineages endemic to the Pacific during the period of reduced abundance and have subsequently colonized the Atlantic several times. Results highlight the apparent impact of past climate change, and suggest selection and hitchhiking are not the sole processes responsible for low mtDNA diversity in this highly social species.