Many viruses are known to form cellular compartments, also called viral factories. Paramyxoviruses, including measles virus, colocalize their proteomic and genomic material in puncta in infected cells. We demonstrate that purified nucleoproteins (N) and phosphoproteins (P) of measles virus form liquid-like membraneless organelles upon mixing in vitro. We identify weak interactions involving intrinsically disordered domains of N and P that are implicated in this process, one of which is essential for phase separation. Fluorescence allows us to follow the modulation of the dynamics of N and P upon droplet formation, while NMR is used to investigate the thermodynamics of this process. RNA colocalizes to droplets, where it triggers assembly of N protomers into nucleocapsid-like particles that encapsidate the RNA. The rate of encapsidation within droplets is enhanced compared to the dilute phase, revealing one of the roles of liquid-liquid phase separation in measles virus replication.