Whether non-native species proliferate to pest status can depend on top-down control from native predators. Among epifaunal molluscs, the shell serves as a main line of anti-predator defence and shell strength may determine the ease with which generalist predators can penetrate prey. We assessed whether, in eastern Australia, the faster growth of the non-native Pacific oyster, Crassostrea gigas, than that of the native Saccostrea glomerata comes at the cost of reduced investment in shell thickening, rendering the non-native oyster more susceptible to a generalist predator, the muricid gastropod Morula marginalba. Laboratory tests confirmed that among larger (>50-mm shell height) oysters, the shells of C. gigas were weaker than those of similar-sized S. glomerata. There were, however, no differences in shell strength or thickness between smaller S. glomerata and C. gigas of the size consumed by M. marginalba. In the absence of shell-strength differences among smaller oysters, M. marginalba preferentially consumed native over non-native oysters. When, however, M. marginalba had no choice of prey item, C. gigas was consumed at the same rate as the native oyster. Our results add to growing evidence that the invasion of C. gigas in eastern Australian estuaries is, at present, causing minimal disruption to trophic relationships.