Measles virus is a highly infectious, enveloped, pleomorphic virus. We combined electron cryotomography with subvolume averaging and immunosorbent electron microscopy to characterize the 3D ultrastructure of the virion. We show that the matrix protein forms helices coating the helical ribonucleocapsid rather than coating the inner leaflet of the membrane, as previously thought. The ribonucleocapsid is folded into tight bundles through matrix-matrix interactions. The implications for virus assembly are that the matrix already tightly interacts with the ribonucleocapsid in the cytoplasm, providing a structural basis for the previously observed regulation of RNA transcription by the matrix protein. Next, the matrix-covered ribonucleocapsids are transported to the plasma membrane, where the matrix interacts with the envelope glycoproteins during budding. These results are relevant to the nucleocapsid organization and budding of other paramyxoviruses, where isolated matrix has been observed to form helices.