Cultivated bivalves are hugely important not only because of their economic value, but also due to their impacts on natural ecosystems. The Pacific oyster (Crassostrea gigas) is the world's most heavily cultivated shellfish species and has been introduced to all continents except Antarctica for aquaculture. We therefore used a medium density single nucleotide polymorphism (SNP) array to investigate the genetic structure of this species in Europe, where it was introduced during the 1960s and has since become a prolific invader of coastal ecosystems across the continent. We analyzed 21,499 polymorphic SNPs in 232 individuals from 23 localities spanning a latitudinal cline from Portugal to Norway and including the source populations of Japan and Canada. We confirmed the results of previous studies by finding clear support for a southern and a northern group, with the former being indistinguishable from the source populations indicating the absence of a pronounced founder effect. We furthermore conducted a large-scale comparison of wild and hatchery populations to reveal substantial genetic differences including significantly higher levels of inbreeding in some but not all of the hatchery populations. These findings were confirmed by a smaller but representative SNP dataset generated using restriction site associated DNA sequencing. We therefore conclude that genomic approaches can generate increasingly detailed insights into the genetics of invasive populations, while also providing a novel window on how hatchery propagation may influence inbreeding, with important economic and management implications.