Physics-informed neural networks (PINNs) have become an important tool in computational mechanics for solving partial differential equations in a mesh-free manner. They have been successfully applied to a wide range of solid and structural mechanics problems. Nevertheless, the training of PINNs for higher-order equations often faces practical difficulties, including high computational cost, sensitivity to hyperparameters, and numerical instability caused by the evaluation of high-order derivatives. These challenges motivate the exploration of alternative physics-informed learning strategies that are better suited for such problems. In the current investigation, a Physics-Informed Holomorphic Neural Network (PIHNN) framework is investigated for the solution of Kirchhoff plate bending problems governed by biharmonic equations. The approach is based on complex-valued neural networks designed to approximate holomorphic functions. By construction, the network satisfies the Cauchy–Riemann conditions, which allows the governing equations to be fulfilled inherently, while boundary conditions are imposed explicitly. As a result, the training process relies solely on boundary data, and the direct evaluation of high-order derivatives inside the domain is avoided. The proposed methodology builds upon the recently introduced PIHNN formulation for two-dimensional linear elasticity problems and extends its application to plate bending models of practical interest in computational mechanics [1]. In order to evaluate applicability and robustness of the proposed framework, several representative Kirchhoff plate configurations with various boundary conditions and loading scenarios are investigated. The numerical investigations show the potential of PIHNNs as an efficient and stable alternative to standard PINN formulations for higher-order boundary value problems. The presented framework offers a promising basis for further investigations of higher-order boundary value problems in structural mechanics.