With the transformation of the energy market from the traditional vertical integrated structure to the interactive competitive structure, the traditional centralized optimization method makes it difficult to reveal the interactive behavior of multi-agent integrated energy systems (MAIES). In this paper, a master–slave game optimal scheduling strategy of MAIES is proposed based on the integrated demand response. Firstly, a master–slave game framework of MAIES is established with an energy management agent as leader, an energy operation agent, an energy storage agent, and a user aggregation agent as followers. Secondly, in view of the wind and solar uncertainty, the Monte Carlo method is used to generate random scenarios, and the k-means clustering method and pre-generation elimination technology are used for scenario reduction. Then, according to different flexible characteristics of loads, a multi-load and multi-type integrated demand response model including electric, thermal, and cold energy is built to fully utilize the regulation role of flexible resources. On this basis, the transaction decision-making models of each agent are constructed, and the existence and uniqueness of the Stackelberg equilibrium solution are proved. Finally, the case simulations demonstrate the effectiveness of the proposed optimal scheduling strategy of MAIES. Compared to the scenario without considering the wind and solar uncertainty and the integrated demand response, the rate of renewable energy curtailment was reduced by 6.03% and the carbon emissions of the system were reduced by 1335.22 kg in the scenario considering the proposed method in this paper.