Present manuscript undergoes with the investigation of the wave propagation features of smart magnetostrictive sandwich nanoplates (MSNPs) with regard to the influences of small scale in the context of the so-called nonlocal strain gradient theory (NSGT) of elasticity. The under observation continuous system, i.e. a thin-type one, is modeled via the Kirchhoff-Love theorem incorporated with the dynamic form of the principle of virtual work considering the impacts of both thermal and viscose losses on the dispersion characteristics of the nanostructure. Once the modified size-dependent constitutive equations are inserted into the motion equations, the final governing equations of the problem are attained. Thereafter, an analytical dispersion solution will be employed for the purpose of solving the dynamic problem to extract the wave response of the system. In order to examine the accuracy of the presented results, the natural frequencies obtained from this methodology are compared with those reported in the open literature. According to the presented illustrations, it can be declared that the magnetostriction can affect the dispersion responses of the smart nanoplate in low wave numbers.