The relatedness structure of animal populations is thought to be a critically important factor underlying the evolution of mating systems and social behaviours. While previous work has shown that population structure is shaped by many biological processes, few studies have investigated how these factors vary over time. Consequently, we explored the fine-scale spatiotemporal genetic structure of an intensively studied population of cooperatively breeding banded mongooses (Mungos mungo) over a 10-year period. Overall population structure was strong (average FST = 0.129) but groups with spatially overlapping territories were not more genetically similar to one another than noncontiguous groups. Instead, genetic differentiation was associated with historical group-fission (budding) events, with new groups diverging from their parent groups over time. Within groups, relatedness was high within but not between the sexes, although the latter increased over time since group formation due to group founders being replaced by philopatric young. This trend was not mirrored by a decrease in average offspring heterozygosity over time, suggesting that close inbreeding may often be avoided, even when immigration into established groups is virtually absent and opportunities for extra-group matings are rare. Fine-scale spatiotemporal population structure could have important implications in social species, where relatedness between interacting individuals is a vital component in the evolution of patterns of inbreeding avoidance, reproductive skew and kin-selected helping and harming.