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This paper presents a nonlocal theoretical model of magneto-elastic phononic crystal (PC) nanoplates to investigate the size-dependent band structure based on the nonlocal theory and Kirchhoff plate theory. The governing equation incorporating the nonlocal effect and magneto-elastic coupling is obtained by the Hamilton's principle and plane wave expansion method. The influence of nonlocal effect and magneto-elastic coupling on band structure of Terfenol-D/epoxy PC nanoplates is studied. The results show the edges and width of band gap increases with the improvement of nonlocal parameter, leading to a promotive influence of nonlocal effect on band gap. Meanwhile, the magneto-elastic coupling plays an important role in regulating band gap with nonlocal effect. The greater the magnetic field and compressive pre-stress can be applied, the larger the band gap is obtained. Consequently, the proposed nonlocal model can be beneficial for flexible tunability of elastic wave and functional design of PC nanodevices in multi-field environments.