Fast evolution of the SARS-CoV-2 virus provides us with unique information about the patterns of genetic changes in a single pathogen in the timescale of months. This data is used extensively to track the phylodynamic of the pandemic's spread and its split into distinct clades. Here we show that the patterns of SARS-CoV-2 virus mutations along its genome are closely correlated with the structural features of the coded proteins. We show that the foldability of proteins' 3D structures and conservation of their functions are the universal factors driving evolutionary selection in protein-coding genes. Insights from the analysis of mutation distribution in the context of the SARS-CoV-2 proteins' structures and functions have practical implications including evaluating potential antigen epitopes or selection of primers for PCR-based COVID-19 tests.