Several evolutionary theories predict that rates of morphological change should be positively associated with the rate at which new species arise. For example, the theory of punctuated equilibrium proposes that phenotypic change typically occurs in rapid bursts associated with speciation events. However, recent phylogenetic studies have found little evidence linking these processes in nature. Here we demonstrate that rates of species diversification are highly correlated with the rate of body size evolution across the 30,000+ living species of ray-finned fishes that comprise the majority of vertebrate biological diversity. This coupling is a general feature of fish evolution and transcends vast differences in ecology and body-plan organization. Our results may reflect a widespread speciational mode of character change in living fishes. Alternatively, these findings are consistent with the hypothesis that phenotypic 'evolvability' - the capacity of organisms to evolve - shapes the dynamics of speciation through time at the largest phylogenetic scales.