Measles virus (MV) is still an imposing threat to public health. The matrix (M) protein has been shown not only to function as a structure block in the assembled MV virions, but also to regulate viral RNA synthesis, playing an important role in MV's replication and assembly. In the present study, we generated a panel of IgG monoclonal antibodies (MAbs) against M protein and successfully obtained one IgA MAb (5H7) from the IgG panel. Employing the polarized Vero cells grown in the two-chamber transwell model, we investigated whether M-specific 5H7 IgA MAb could suppress MV's replication and assembly. The data presented indicate that, while failing to show the activities of traditional neutralization and immune exclusion, M-specific IgA MAb was able to effectively inhibit viral replication by intracellular neutralization (78%), supporting the notion that the M protein is important for MV assembly and replication and implying that the M protein was an effective target antigen. The data also showed that MV had a long entry and assembly phase during viral replication, providing an extended window for IgA intervention. The colocalization of M proteins and M-specific 5H7 IgA MAbs demonstrated that the intracellular neutralization was due to the direct binding of the M-specific 5H7 IgA MAbs to the M proteins. In summary, the present study has added another example showing that IgA antibodies targeting internal viral antigens could proactively participate in mucosal immune protection by intracellular neutralization and has provided evidence that M protein might be included as a target antigen in future MV vaccine design.