An exact closed-form solution for the three-dimensional static deformation and free vibrational response of a simply supported and multilayered quasicrystal (QC) nanoplate with the nonlocal effect is derived. Numerical examples are presented for a homogeneous crystal nanoplate, homogenous QC nanoplate, and sandwich nanoplates with various stacking sequences. Induced by traction boundary conditions, extended displacements and stresses reveal the important role that the nonlocal parameter plays in the structural analysis of nanoquasicrystals (nano-QCs). The natural frequencies and the corresponding mode shapes of the nanoplates further show the influence of stacking sequence and phonon–phason coupling effect. This exact solution is useful for it provides benchmark results to assess the accuracy of finite element nano-QC models and can assist engineers in tuning their quasicrystal nanoplate design.