Hydrogen represents a highly promising alternative energy vehicle that facilitates the transition toward a carbon-neutral economy. However, the current hydrogen storage technologies are both inefficient and costly, which significantly limits the overall efficiency of hydrogen energy systems. The method of storing hydrogen via physical adsorption in Metal-Organic Frameworks (MOFs) has emerged as a particularly promising solution for hydrogen storage, attributed to their extensive surface area and remarkable tunability. Machine learning techniques have demonstrated great potential in screening a theoretically limitless number of MOFs that meet specific hydrogen storage targets, but these models often lack physical consistency. To address this limitation, this study presents a Physics-Informed Neural Network (PINN) that incorporates monotonic relationships between the crystallographic characteristics and hydrogen storage capacity into the neural network architecture to effectively screen the high hydrogen storage capacity MOFs. The performances of the identified top MOFs were validated by the Grand Canonical Monte Carlo simulations. Compared to other machine learning methods, the top MOFs identified by PINN exhibit meaningful crystallographic features via heatmap analysis. The proposed PINN model successfully identified two experimentally synthesized MOFs, LADQEM_CSD17 and LADQEM01_CSD17, that meet the targets for onboard hydrogen storage systems established by the U.S. Department of Energy for the year 2025.