<p>A comprehensive numerical framework is presented to study the geometrically nonlinear free vibration behavior of functionally graded (FG) microplates with arbitrary shapes, considering size-dependent effects within Mindlin’s strain-gradient elasticity theory. The proposed formulation employs the first-order shear deformation plate theory in conjunction with Hamilton’s principle to derive the general nonlinear governing equations. The strain-gradient tensors and their conjugate higher-order stresses are represented in an efficient vector–matrix form, enabling a computationally tractable implementation of the variational differential quadrature (VDQ) method for domains of irregular geometry. By assigning appropriate gradient-based material parameters, the developed model can seamlessly degenerate to simplified size-dependent continuum theories or recover the predictions of the classical theory. The free vibration response is determined by solving the resulting nonlinear eigenvalue problem using a reduced-order Galerkin approach followed by a time-periodic discretization and the pseudo arc-length method. Parametric studies are carried out to examine the influence of key factors, including geometrical shape, boundary conditions, FG index, and length scale parameters, on the fundamental frequencies and nonlinear frequency–amplitude relations. The results highlight significant sensitivity of the nonlinear vibration response to both the material gradation and the microscale length parameters, underscoring the necessity of using higher-order strain-gradient models for accurate prediction of FG microplate dynamics.</p>