Automated feature engineering (AutoFE) is used to automatically create new features from original features to improve predictive performance without needing significant human intervention and domain expertise. Many algorithms exist for AutoFE, but very few approaches exist for the federated learning (FL) setting where data is gathered across many clients and is not shared between clients or a central server. We introduce AutoFE algorithms for the horizontal, vertical, and hybrid FL settings, which differ in how the data is gathered across clients. To the best of our knowledge, we are the first to develop AutoFE algorithms for the horizontal and hybrid FL cases, and we show that the downstream test scores of our federated AutoFE algorithms is close in performance to the case where data is held centrally and AutoFE is performed centrally.