Free vibration of plates is analyzed using isogeometric analysis (IGA) combined with model order reduction (MOR). The displacement in the plate plane is simulated by non-uniform rational B-spline (NURBS) functions, while the displacement across the plate thickness is represented via the generalized shear deformation theory (GSDT). Accordingly, both thick and thin plates can be well handled without using any shear correction factors as in classical plate theories. Moreover, Guyan’s method-based MOR technique is built based on the IGA to analyze the plates’ free vibration. This scheme helps to resolve the free vibration equation system relied upon key degrees of freedom (DOFs) instead of all DOFs. This methodology is very suitable in practice, especially for structural health monitoring (SHM) in the case of sensor limitations. A square plate is presented to prove the capability of the proposed methodology. Results obtained by MOR and full model based on the IGA are compared for verification. Outcomes have revealed that the only first four frequencies given by MOR-based IGA are reliable. This is because the above MOR techniques neglect rotational inertia masses in the mass matrix.