Genome-wide association studies (GWASs) have discovered a large number of genetic variants in human patients with disease. Thus, predicting the impact of these variants is important for sorting disease-associated variants from neutral variants. Current methods to predict the mutational impacts depend on evolutionary conservation at the mutation site, which is determined using homologous sequences and based on the assumption that variants at well-conserved sites have high impacts. However, many disease-associated variants at less conserved but functionally important sites cannot be predicted by the current methods. Here, we present a method to find disease-associated variants at less conserved sites by predicting the mutational impacts using evolutionarily coupling analysis. Functionally important and evolutionarily coupled sites often have compensatory variants on cooperative sites to avoid loss of function. We found that our method identified known intolerant variants in a diverse group of proteins. Furthermore, at less conserved sites, we identified disease-associated variants that are not identified using conservation-based methods. These newly identified disease-associated variants were frequently found at protein interaction interfaces, where species-specific mutations often alter interaction specificity. This work presents a means to identify less conserved disease-associated variants, and provides insight into the relationship between evolutionarily coupled sites and human disease-associated variants.