Incorporating species' eco-evolutionary responses to human-caused disturbances remains a challenge in marine management efforts. A prerequisite is knowledge of geographic structure and scale of genetic diversity and connectivity - the so-called seascape genetic patterns. The Baltic Sea is an excellent model system for studies linking seascape genetics with effects of anthropogenic stress. However, seascape genetic patterns in this area are only described for a few species and are completely unknown for invertebrate herbivores, which constitute a critical part of the ecosystem. This information is crucial for sustainable management, particularly under future scenarios of rapid environmental change. Here, we investigate the population genetic structure among 31 locations throughout the Baltic Sea, of which 45 % were located in marine protected areas, in one of the most important herbivores of this region, the isopod crustacean Idotea balthica, using an array of 33,774 genome-wide SNP markers derived from 2b-RAD sequencing. In addition, we generate a biophysical connectivity matrix for I. balthica from a combination of oceanographic current models and estimated life history traits. We find strong population structure on scales of hundreds of kilometers across the Baltic Sea, where genomic patterns in most cases closely match biophysical connectivity, indicating passive transport with oceanographic currents as an important mean of dispersal in this species. We also find successively reduced genetic diversity in terms of heterozygosity from the entrance towards the innermost parts of the Baltic Sea, suggesting multiple bottlenecks that presumably took place during the initial range expansion following the postglacial opening of the Baltic Sea. Both of these results provide crucial information for management of a key ecosystem species under expected changes in temperature and salinity following global climate change in a marine coastal area.