Accurate prediction of crop above-ground biomass (AGB) under water stress is critical for monitoring crop productivity, guiding irrigation, and supporting climate-resilient agriculture. Data-driven models scale well but often lack interpretability and degrade under distribution shift, whereas process-based crop models (e.g. DSSAT, APSIM, LINTUL5) require extensive calibration and are difficult to deploy over large spatial domains. To address these limitations, we propose AgriPINN, a process-informed neural network that integrates a biophysical crop-growth differential equation as a differentiable constraint within a deep learning backbone. This design encourages physiologically consistent biomass dynamics under water-stress conditions while preserving model scalability for spatially distributed AGB prediction. AgriPINN recovers latent physiological variables, including leaf area index (LAI), absorbed photosynthetically active radiation (PAR), radiation use efficiency (RUE), and water-stress factors, without requiring direct supervision. We pretrain AgriPINN on 60 years of historical data across 397 regions in Germany and fine-tune it on three years of field experiments under controlled water treatments. Results show that AgriPINN consistently outperforms state-of-the-art deep-learning baselines (ConvLSTM-ViT, SLTF, CNN-Transformer) and the process-based LINTUL5 model in terms of accuracy (RMSE reductions up to $43\%$) and computational efficiency. By combining the scalability of deep learning with the biophysical rigor of process-based modeling, AgriPINN provides a robust and interpretable framework for spatio-temporal AGB prediction, offering practical value for planning of irrigation infrastructure, yield forecasting, and climate-adaptation planning.