Acts as a negative regulator for transcription and replication by sticking to the nucleocapsid. This effect might be regulated by the cytoplasmic interaction with tubulin that dissociates the M protein from the nucleocapsid (By similarity). Plays a crucial role in virion assembly and budding. Forms a shell at the inner face of the plasma membrane and concentrates the HN and F glycoproteins. Homomultimer. Binds to the cytoplasmic regions of F and HN proteins. Interacts with nucleocapsid. Interacts with human alpha-tubulin and beta-tubulin. Interacts with host ANP32B. During bud formation, associates at the inner side of the plasma membrane of infected cells. Late-budding domains (L domains) are short sequence motifs essential for viral particle budding. They recruit proteins of the host ESCRT machinery (Endosomal Sorting Complex Required for Transport) or ESCRT-associated proteins. The matrix protein contains one L domain: a YLDL motif (By similarity). A large portion is phosphorylated in the cytoplasm, but not in virion. However, this phosphorylation is not essential for virus replication (By similarity). Belongs to the morbillivirus/respirovirus/rubulavirus M protein family.