Background The Mediterranean mussel Mytilus galloprovincialis is an ecologically and economically relevant edible marine bivalve, highly invasive and resilient to biotic and abiotic stressors causing recurrent massive mortalities in other bivalves. Although these traits have been recently linked with the maintenance of a high genetic variation within natural populations, the factors underlying the evolutionary success of this species remain unclear. Results Here, after the assembly of a 1.28-Gb reference genome and the resequencing of 14 individuals from two independent populations, we reveal a complex pan-genomic architecture in M. galloprovincialis, with a core set of 45,000 genes plus a strikingly high number of dispensable genes (20,000) subject to presence-absence variation, which may be entirely missing in several individuals. We show that dispensable genes are associated with hemizygous genomic regions affected by structural variants, which overall account for nearly 580 Mb of DNA sequence not included in the reference genome assembly. As such, this is the first study to report the widespread occurrence of gene presence-absence variation at a whole-genome scale in the animal kingdom. Conclusions Dispensable genes usually belong to young and recently expanded gene families enriched in survival functions, which might be the key to explain the resilience and invasiveness of this species. This unique pan-genome architecture is characterized by dispensable genes in accessory genomic regions that exceed by orders of magnitude those observed in other metazoans, including humans, and closely mirror the open pan-genomes found in prokaryotes and in a few non-metazoan eukaryotes.