Event trigger extraction is a natural language processing (NLP) task of practical utility, which requires systems to detect and label the lexical instantiation of an event. Existing deep learning-based event trigger extraction approaches that require large-scale data for model training achieve limited success in some privacy-sensitive domains, due to the challenge of aggregating data distributed among various owners. Federated learning (FL) has emerged as a secure distributed machine learning paradigm that addresses the issue of data silos in building a joint model, with the advantages of security aggregation mechanism. Therefore, we define the task of FL-based event trigger extraction and propose a novel federated method named FedETE to solve the current difficulties. We also introduce the idea of weak privacy of the event trigger to craft the architecture of FedETE which optimizes the traditional FL training methods (Server-Client). Extensive experiments show that the event trigger extraction model trained by FedETE achieves promising results compared to centralized methods and traditional FL methods, as well as local methods. To our knowledge, FedETE is the first to apply FL in the event trigger extraction task.