Motivated by the recent successful formation of the MoSi2N4 monolayer (Hong et al 2020 Science 369, 670), the structural, electronic, and magnetic properties of MoSi2N4 nanoribbons (NRs) is investigated for the first time. The band structure calculations showed spin-polarization in zigzag edges and a non-magnetic semiconducting character in armchair edges. For armchair-edges, we identify an indirect to direct bandgap shift compared to the MoSi2N4 monolayer, and its energy gap increases with increasing NR width. Anisotropic electrical and magnetic behaviors are observed via band structure calculations at the zigzag and armchair edges, where, surprisingly, for one type of zigzag-edge configuration, we identifed a Dirac-semimetal character. The appearance of magnetism and Dirac-semimetal in MoSi2N4 ribbons can give rise to novel physical properties, which could be helpful in applications for next-generation electronic devices.