All viruses on Earth rely on host cell machinery for replication, a process that involves a complex self-assembly mechanism. Our aim here is to scrutinize in real time the growth of icosahedral viral nucleocapsids with single-molecule precision. Using total internal reflection fluorescence microscopy, we probed the binding and unbinding dynamics of fluorescently labeled capsid subunits on hundreds of immobilized viral RNA molecules simultaneously at each time point. A step-detection algorithm combined with statistical analysis allowed us to estimate microscopic quantities such as the equilibrium binding rate and mean residence time, which are otherwise inaccessible through traditional ensemble-averaging techniques. Additionally, we could estimate a set of rate constants modeling the growth kinetics from nonequilibrium measurements, and we observed an acceleration in growth caused by the electrostatic screening effect of monovalent salts. Single-molecule fluorescence imaging will be crucial for elucidating virus self-assembly at the molecular level, particularly in crowded, cell-like environments.