The space–air–ground integrated network (SAGIN) is considered to be a significant framework for realizing the vision of “6G intelligent connection of all things.” A typical SAGIN consists of three parts: a space-based network composed of various orbiting satellites, an air-based network composed of aircraft, and a traditional ground-based network. Considering the cost of satellite launch, the network needs to be flexible and controllable. In order to ensure that the ground can handle satellite anomalies in real time by program, it is necessary to introduce in-orbit programmable networks, such as the software-defined network (SDN). In the network management architecture, if the controller plane in the SDN adopts the flat management scheme, the expansion of the control plane is limited due to the low efficiency of data synchronization among controllers. Compared with controller deployments on terrestrial networks, multicontroller deployments in the SAGIN face the following problems: the dynamic change of the satellite network topology, the large-scale network nodes, the increase or decrease in the number of aerial vehicles, and the unbalanced distribution of ground users. Therefore, it is of great significance to study how to optimize the deployment of multiple controllers in the SDN-enabled SAGIN. This article introduces an SDN into the SAGIN and designs a hierarchical domain-based SDN-enabled SAGIN architecture. A multicontroller deployment strategy for the hierarchical domain-based SDN-enabled SAGIN is proposed. First, we divide the SDN control plane into two layers, i.e., the primary controller layer is deployed on the ground network and the secondary on the space-based network. The SDN data plane is composed of space-based, air-based, and ground-based networks. Second, considering the average network delay and the controller load, a multiobjective optimization model is constructed. To determine the number of controllers and the relative positions of switch nodes and controllers, the clustering algorithm based on k -means is adopted to initially divide the data plane. Finally, to improve the global search ability of the algorithm, a multiobjective optimization algorithm based on a genetic algorithm is adopted. The simulation results show that the proposed strategy is effective in reducing the average network delay and improving the controller load balance. Compared to other algorithms, the average network delay is reduced by 13.3% and the controller load is improved by 10.33%.