Many high-throughput experimental technologies have been developed to assess the effects of large numbers of mutations (variation) on phenotypes. However, designing functional assays for these methods is challenging, and systematic testing of all combinations is impossible, so robust methods to predict the effects of genetic variation are needed. Most prediction methods exploit evolutionary sequence conservation but do not consider the interdependencies of residues or bases. We present EVmutation, an unsupervised statistical method for predicting the effects of mutations that explicitly captures residue dependencies between positions. We validate EVmutation by comparing its predictions with outcomes of high-throughput mutagenesis experiments and measurements of human disease mutations and show that it outperforms methods that do not account for epistasis. EVmutation can be used to assess the quantitative effects of mutations in genes of any organism. We provide pre-computed predictions for ∼7,000 human proteins at http://evmutation.org/.