Anomaly detection is an important task for medical image analysis, which can alleviate the reliance of supervised methods on large labelled datasets. Most existing methods use a pixel-wise self-reconstruction framework for anomaly detection. However, there are two challenges of these studies: 1) they tend to overfit learning an identity mapping between the input and output, which leads to failure in detecting abnormal samples; 2) the reconstruction considers the pixel-wise differences which may lead to an undesirable result. To mitigate the above problems, we propose a novel heterogeneous Auto-Encoder (Hetero-AE) for medical anomaly detection. Our model utilizes a convolutional neural network (CNN) as the encoder and a hybrid CNN-Transformer network as the decoder. The heterogeneous structure enables the model to learn the intrinsic information of normal data and enlarge the difference on abnormal samples. To fully exploit the effectiveness of Transformer in the hybrid network, a multi-scale sparse Transformer block is proposed to trade off modelling long-range feature dependencies and high computational costs. Moreover, the multi-stage feature comparison is introduced to reduce the noise of pixel-wise comparison. Extensive experiments on four public datasets (i.e., retinal OCT, chest X-ray, brain MRI, and COVID-19) verify the effectiveness of our method on different imaging modalities for anomaly detection. Additionally, our method can accurately detect tumors in brain MRI and lesions in retinal OCT with interpretable heatmaps to locate lesion areas, assisting clinicians in diagnosing abnormalities efficiently.