Adaptive radiations are characterised by the diversification and ecological differentiation of species, and replicated cases of this process provide natural experiments for understanding the repeatability and pace of molecular evolution. During adaptive radiation, genes related to ecological specialisation may be subject to recurrent positive directional selection. However, it is not clear to what extent patterns of lineage-specific ecological specialisation (including phenotypic convergence) are correlated with shared signatures of molecular evolution. To test this, we sequenced whole exomes from a phylogenetically dispersed sample of 38 murine rodent species, a group characterised by multiple, nested adaptive radiations comprising extensive ecological and phenotypic diversity. We found that genes associated with immunity, reproduction, diet, digestion and taste have been subject to pervasive positive selection during the diversification of murine rodents. We also found a significant correlation between genome-wide positive selection and dietary specialisation, with a higher proportion of positively selected codon sites in derived dietary forms (i.e. carnivores and herbivores) than in ancestral forms (i.e. omnivores). Despite striking convergent evolution of skull morphology and dentition in two distantly related worm-eating specialists, we did not detect more genes with shared signatures of positive or relaxed selection than in a non-convergent species comparison. While a small number of the genes we detected can be incidentally linked to craniofacial morphology or diet, protein-coding regions are unlikely to be the primary genetic basis of this complex convergent phenotype. Our results suggest a link between positive selection and derived ecological phenotypes, and highlight specific genes and general functional categories that may have played an integral role in the extensive and rapid diversification of murine rodents.