Plays a crucial role in virion assembly and budding. Forms a shell at the inner face of the plasma membrane (PubMed:17005661, PubMed:17204159, PubMed:19000317). Transits through the host nucleus before gaining the functional ability to localize and bud from the plasma membrane (PubMed:21085610). Mediates together with fusion protein the incorporation of the glycoprotein to the viral particles (PubMed:28250132). Participates also in the inhibition of the host interferon type I antiviral response by interacting with and thereby inhibiting host TRIM6 (PubMed:27622505). Homomultimer (PubMed:17005661). Interacts with host TRIM6; this interaction inhibits the IKBKE-dependent activation of the type I interferon signaling pathway (PubMed:27622505). Interacts with host ANP32B; this interaction promotes M nuclear localization (By similarity). During bud formation, associates at the inner side of the plasma membrane of infected cells. Nuclear-cytoplasmic trafficking is essential for budding and requires matrix ubiquitination. Ubiquitinated; regulates matrix nuclear export. Belongs to the morbillivirus/respirovirus/rubulavirus M protein family.