In digital healthcare applications, anomaly detection is an important task to be taken into account. For instance, in ECG (Electrocardiogram) analysis, the aim is often to detect abnormal ECG signals that are considered outliers. For such tasks, it has been shown that deep learning models such as Autoencoders (AEs) and Variational Autoencoders (VAEs) can provide state-of-the-art performance. However, they suffer from certain limitations. For example, the trivial method of threshold selection does not perform well if we do not know the reconstruction loss distribution in advance. In addition, since healthcare applications rely on highly sensitive personal information, data privacy concerns can arise when data are collected and processed in a centralized machine-learning setting. Hence, in order to address these challenges, in this paper, we propose AnoFed, a novel framework for combining the transformer-based AE and VAE with the Support Vector Data Description (SVDD) in a federated setting. It can enhance privacy protection, improve the explainability of results and support adaptive anomaly detection. Using ECG anomaly detection as a typical application of the framework in healthcare, we conducted experiments to show that the proposed framework is not only effective (in terms of the detection performance) but also efficient (in terms of computational costs), compared with a number of state-of-the-art methods in the literature. AnoFed is very lightweight in terms of the number of parameters and computation, hence it can be used in applications with resource-constrained edge devices.