Electrification has emerged as a pivotal trend in the energy transition to address climate change, leading to a substantial surge in the demand for batteries. Accurately predicting the internal states and performance of batteries assumes paramount significance, as it ensures the safe and stable operation of batteries and informs decision-making processes, such as optimizing battery operation for arbitrage opportunities. However, current models struggle to strike a balance between precision and computational efficiency or are limited in their applicability to specific scenarios. We aim to adopt a physics-informed deep operator network (PI-DeepONet) for internal battery state estimation based on the rigorous P2D model, which can simultaneously achieve high precision and computational efficiency. Furthermore, it exhibits promising prospects for extension beyond lithium-ion batteries to encompass various battery technologies.