Multicast communication technology is widely applied in wireless environments with a high device density. Traditional wireless network architectures have difficulty flexibly obtaining and maintaining global network state information and cannot quickly respond to network state changes, thus affecting the throughput, delay, and other QoS requirements of existing multicasting solutions. Therefore, this paper proposes a new multicast routing method based on multiagent deep reinforcement learning (MADRL-MR) in a software-defined wireless networking (SDWN) environment. First, SDWN technology is adopted to flexibly configure the network and obtain network state information in the form of traffic matrices representing global network links information, such as link bandwidth, delay, and packet loss rate. Second, the multicast routing problem is divided into multiple subproblems, which are solved through multiagent cooperation. To enable each agent to accurately understand the current network state and the status of multicast tree construction, the state space of each agent is designed based on the traffic and multicast tree status matrices, and the set of AP nodes in the network is used as the action space. A novel single-hop action strategy is designed, along with a reward function based on the four states that may occur during tree construction: progress, invalid, loop, and termination. Finally, a decentralized training approach is combined with transfer learning to enable each agent to quickly adapt to the dynamic changes of network link information and accelerate convergence. Simulation experiments show that MADRL-MR outperforms existing algorithms in terms of throughput, delay, packet loss rate, etc., and can establish more intelligent multicast routes. Code and model are available at https://github.com/GuetYe/MADRL-MR_code.