This paper deals with the free vibration response of rectangular functionally graded material sandwich nanoplates with simply supported boundary conditions. The material properties of the FGM layers are temperature-dependent and supposed to be graded continuously along the thickness direction. A simple power-law distribution in terms of the volume fractions of the material constituents is employed to obtained the effective material properties. Eringen’s nonlocal elasticity model is incorporated in order to take into account the small size effects. Two types of functionally graded material sandwich nanoplates are considered: a sandwich with functionally graded material face layers and homogeneous core, and a sandwich with homogeneous face layers and functionally graded material core. The equations of motion of the functionally graded material sandwich nanoplates are derived by using the higher shear deformation theory and the Hamilton’s variational principle, and solved using the Navier’s solutions. Several numerical results indicate the influence of the power–law index, the nonlocal parameter, the geometrical parameters of the nanoplate, and the temperature variation on the free vibration response are presented.