The Galapagos shark (Carcharhinus galapagensis) is one of over thirty shark species inhabiting the Galápagos Marine Reserve (GMR), where it is a priority species for conservation. Identifying stock structure and effective population size for species-specific management and effective conservation of this top predator is important. We examined stock structure, connectivity and effective population size of Galapagos sharks among GMR locations using genome-wide neutral Single Nucleotide Polymorphism (8103 SNP) and mtDNA markers. Potential historical gene flow and/or sex-biased dispersal were also examined using the mitochondrial control region (997 bp). Cluster analyses of neutral SNPs revealed two differentiated stocks in the GMR—a western (Isabela Island) and eastern (San Cristóbal and Santa Cruz Islands) stock. Effective population size (Ne) estimates of approximately 200 suggest these populations are susceptible to ongoing natural and anthropogenic stressors and are of concern for long term resilience of populations. Mitochondrial DNA failed to identify distinct stocks, with AMOVA analyses indicating most genetic variation occurs within, rather than among locations. This pattern of genome-wide nuclear (but not mtDNA) discrimination among neighbouring islands either points to possible sex-biased dispersal by females or identifies limitations of the single organelle mtDNA marker at such small spatial scales. Regional differences across the archipelago or in behaviour may be implicated in the observed population structure. Further research focusing on a larger, Pacific wide analysis of population connectivity and effective population size at a broader spatial scale is required, to estimate the extent of discreteness and potential local adaptation. Potential adaptive units (AUs) in Galapagos sharks should ultimately be identified to leverage adaptive management and fisheries forensics applications.