Driven by the global Sustainable Development Goals, predicting the long-term trend of carbon emissions in the industrial sector has important reference value for managing national macroeconomic and reducing carbon emissions. To address the potential privacy leakage problem when using multisource industrial big data for carbon emission prediction, a federated learning method was introduced for carbon emission prediction research. However, owing to the variability in individual data providers, using all clients indiscriminately to train the federated model may hinder the computational efficiency of federated learning. To improve the accuracy and computational efficiency of the prediction model, a federated learning method based on SARIMA clustering was proposed. First, a trend was fitted to all clients based on the SARIMA model and the clients were grouped into different clusters based on the fitting results. Second, a federated bidirectional long short-term memory calculation was implemented for different client combinations using a federated averaging algorithm. Extensive experimental results on real datasets show that combining SARIMA and the federated averaging algorithm protects the data privacy of clients and improves the convergence speed and accuracy of the federated learning carbon emission prediction model. Within the optimal set of clusters (Cluster 0), the mean absolute error and mean square error improved by 63.32% and 79.27%, respectively, and the convergence speed of the model improved by 73.17%. This study further enriches the methodological system of carbon emission prediction and provides methodological support for relevant departments to use multisource big data in the industry for carbon emission prediction.