Multi-microgrid collaborative scheduling can promote the local consumption of renewable energy in the smart grid and reduce the operating costs of the power grid park. At the same time, the access of the distributed energy storage (ES) system provides an opportunity to further enhance the park’s peak shaving and valley filling capacity, thereby reducing costs. However, the uncertainty of photovoltaic (PV) power generation and load demand seriously affects the profit maximization of the microgrid in the park. To address this challenge, this paper proposes a stochastic optimal scheduling strategy for industrial park smart microgrids with multiple transformers based on the information gap decision theory (IGDT). We first introduce a revenue maximization model for industrial parks, incorporating a two-part tariff system and distributed ES. Subsequently, we employ an envelope constraint model to accurately represent the uncertainty associated with PV generation and load demand. By integrating these components, we establish the IGDT stochastic optimization scheduling model for industrial parks with multiple transformers. Finally, we simulate and analyze the performance of the proposed IGDT model under various cost deviation factors during typical spring and summer days. The simulation results demonstrate the effectiveness of the proposed control strategy in mitigating the impact of PV generation and load uncertainty on industrial parks. The IGDT-based scheduling approach provides an efficient solution for maximizing revenue and enhancing the operational stability of industrial park microgrids.