A fundamental requirement for full autonomy in mobile robots is accurate navigation even in situations where satellite navigation or cameras are unavailable. In such practical situations, relying only on inertial sensors will result in navigation solution drift due to the sensors' inherent noise and error terms. One of the emerging solutions to mitigate drift is to maneuver the robot in a snake-like slithering motion to increase the inertial signal-to-noise ratio, allowing the regression of the mobile robot position. In this work, we propose MoRPI-PINN as a physics-informed neural network framework for accurate inertial-based mobile robot navigation. By embedding physical laws and constraints into the training process, MoRPI-PINN is capable of providing an accurate and robust navigation solution. Using real-world experiments, we show accuracy improvements of over 85% compared to other approaches. MoRPI-PINN is a lightweight approach that can be implemented even on edge devices and used in any typical mobile robot application.