Against the backdrop of the rapid development of the energy internet, the role of energy storage systems in grid stability, energy balance, and renewable energy integration has become increasingly important. Among these systems, estimating the state of health (SOH) of battery storage systems, particularly lithium batteries, is crucial for ensuring system reliability and safety. While data-driven methods have poor interpretability and physics-based models are computationally expensive, physics-informed neural networks (PINNs) offer a compromise but struggle with high-dimensional inputs and dynamic variable coupling. This paper proposed a novel Kolmogorov–Arnold networks with physics-informed neural network (KAN-PINN) framework for lithium-ion battery SOH estimation. By leveraging KANs’ superior high-dimensional approximation capabilities and embedding the Verhulst model as a physical constraint, the framework enhances nonlinear representation while ensuring predictions adhere to degradation physics. Experimental results on a public dataset demonstrate the model’s superiority, achieving an RMSPE of 0.300 and MAE of 1.342%, along with strong interpretability and robustness across battery chemistries and operating conditions.