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Network Virtualization (NV) is an emerging network dynamic planning technique to overcome network rigidity. As its necessary challenge, Virtual Network Embedding (VNE) enhances the scalability and flexibility of the network by decoupling the resources and services of the underlying physical network. For the future multi-domain physical network modeling with the characteristics of dynamics, heterogeneity, privacy, and real-time, the existing related works perform satisfactorily. Federated learning (FL) jointly optimizes the network by sharing parameters among multiple parties and is widely employed in disputes over data privacy and data silos. Aiming at the NV challenge of multi-domain physical networks, this work is the first to propose using FL to model VNE, and presents a VNE architecture based on Horizontal Federated Learning (HFL) (HFL-VNE). Specifically, combined with the distributed training paradigm of FL, we deploy local servers in each physical domain, which can effectively focus on local features and reduce resource fragmentation. A global server is deployed to aggregate and share training parameters, which enhances local data privacy and significantly improves learning efficiency. Furthermore, we deploy the Deep Reinforcement Learning (DRL) model in each server to dynamically adjust and optimize the resource allocation of the multi-domain physical network. In DRL-assisted FL, HFL-VNE jointly optimizes decision-making through specific local and federated reward mechanisms and loss functions. Finally, the superiority of HFL-VNE is proved by combining simulation experiments and comparing it with related works.