Protein solubility problems arise in a wide range of applications, from antibody development to enzyme production, and are linked to several major disorders, including cataracts and Alzheimer's diseases. To assist scientists in designing proteins with improved solubility and better understand solubility-related diseases, we introduce SOuLMuSiC, a computational tool for the fast and accurate prediction of the impact of single-site mutations on protein solubility. Our model is based on a simple artificial neural network that takes as input a series of features, including biophysical properties of wild-type and mutated residues, energetic values computed using various statistical potentials, and mutational scores derived from protein language models. SOuLMuSiC has been trained on a curated dataset of about 700 single-site mutations with known solubility values, collected and manually verified from original literature. It significantly outperforms current state-of-the-art predictors in strict cross validation: the Spearman correlation reaches 0.5 when solubility changes are represented categorically; for the subset with quantitative values, it increases to 0.7. SOuLMuSiC also shows good performance on external datasets containing high-throughput enzyme solubility-related data as well as protein aggregation propensities. In summary, SOuLMuSiC is a valuable tool for identifying mutations that impact protein solubility, and can play a major role in the rational design of proteins with improved solubility and in understanding genetic variants' effect. It is freely available for academic use at http://babylone.ulb.ac.be/SoulMuSiC/.