State-of-the-art deep learning models often fail to generalize in the presence of distribution shifts between training (source) data and test (target) data. Domain adaptation methods are designed to address this issue using labeled samples (supervised domain adaptation) or unlabeled samples (unsupervised domain adaptation). Active learning is a method to select informative samples to obtain maximum performance from minimum annotations. Selecting informative target domain samples can improve model performance and robustness, and reduce data demands. This paper proposes a novel pipeline called ALFREDO (Active Learning with FeatuRe disEntangelement and DOmain adaptation) that performs active learning under domain shift. We propose a novel feature disentanglement approach to decompose image features into domain specific and task specific components. Domain specific components refer to those features that provide source specific information, e.g., scanners, vendors or hospitals. Task specific components are discriminative features for classification, segmentation or other tasks. Thereafter we define multiple novel cost functions that identify informative samples under domain shift. We test our proposed method for medical image classification using one histopathology dataset and two chest X-ray datasets. Experiments show our method achieves state-of-the-art results compared to other domain adaptation methods, as well as state of the art active domain adaptation methods.